Oberhettinger, Fritz
Overview
Works:  55 works in 282 publications in 5 languages and 5,287 library holdings 

Genres:  Mathematical formulae Tables (Data) 
Roles:  Author, Editor 
Classifications:  QA351, 517.5 
Publication Timeline
.
Most widely held works by
Fritz Oberhettinger
Formulas and theorems for the special functions of mathematical physics by
Wilhelm Magnus(
Book
)
26 editions published between 1949 and 1966 in 4 languages and held by 997 WorldCat member libraries worldwide
This is a new and enlarged English edition of the book which, under the title "Formeln und Satze fur die Speziellen Funktionen der mathe matischen Physik" appeared in German in 1946. Much of the material (part of it unpublished) did not appear in the earlier editions. We hope that these additions will be useful and yet not too numerous for the purpose of locating .with ease any particular result. Compared to the first two (German) editions a change has taken place as far as the list of references is concerned. They are generally restricted to books and monographs and accomodated at the end of each individual chapter. Occasional references to papers follow those results to which they apply. The authors felt a certain justification for this change. At the time of the appearance of the previous edition nearly twenty years ago much of the material was scattered over a number of single contributions. Since then most of it has been included in books and monographs with quite exhaustive bibliographies. For information about numerical tables the reader is referred to "Mathematics of Computation", a periodical publis hed by the American Mathematical Society; "Handbook of Mathe matical Functions" with formulas, graphs and mathematical tables National Bureau of Standards Applied Mathematics Series, 55, 1964, 1046 pp., Government Printing Office, Washington, D.C., and FLETCHER, MILLER, ROSENHEAD, Index of Mathematical Tables, AddisonWesley, Reading, Mass.) . There is a list of symbols and abbreviations at the end of the book
26 editions published between 1949 and 1966 in 4 languages and held by 997 WorldCat member libraries worldwide
This is a new and enlarged English edition of the book which, under the title "Formeln und Satze fur die Speziellen Funktionen der mathe matischen Physik" appeared in German in 1946. Much of the material (part of it unpublished) did not appear in the earlier editions. We hope that these additions will be useful and yet not too numerous for the purpose of locating .with ease any particular result. Compared to the first two (German) editions a change has taken place as far as the list of references is concerned. They are generally restricted to books and monographs and accomodated at the end of each individual chapter. Occasional references to papers follow those results to which they apply. The authors felt a certain justification for this change. At the time of the appearance of the previous edition nearly twenty years ago much of the material was scattered over a number of single contributions. Since then most of it has been included in books and monographs with quite exhaustive bibliographies. For information about numerical tables the reader is referred to "Mathematics of Computation", a periodical publis hed by the American Mathematical Society; "Handbook of Mathe matical Functions" with formulas, graphs and mathematical tables National Bureau of Standards Applied Mathematics Series, 55, 1964, 1046 pp., Government Printing Office, Washington, D.C., and FLETCHER, MILLER, ROSENHEAD, Index of Mathematical Tables, AddisonWesley, Reading, Mass.) . There is a list of symbols and abbreviations at the end of the book
Tables of Fourier transforms and Fourier transforms of distributions by
Fritz Oberhettinger(
Book
)
32 editions published between 1957 and 2013 in 3 languages and held by 870 WorldCat member libraries worldwide
This book presents a collection of integrals of the sine, cosine and exponential Fourier transforms of functions f(x). It is the second, considerably enlarged version of the author's previous publication "Tabellen zur Fourier Transformation" (SpringerVerlag 1957). In addition to numerous new results in Parts IIII, a new Part IV has been introduced dealing with problems in mathematical statistics. The aim of the book is to serve as a reference work for all those whose main interest is in the application of Fourier transform methods. These methods have found a wide variety of applications in the natural and technical sciences
32 editions published between 1957 and 2013 in 3 languages and held by 870 WorldCat member libraries worldwide
This book presents a collection of integrals of the sine, cosine and exponential Fourier transforms of functions f(x). It is the second, considerably enlarged version of the author's previous publication "Tabellen zur Fourier Transformation" (SpringerVerlag 1957). In addition to numerous new results in Parts IIII, a new Part IV has been introduced dealing with problems in mathematical statistics. The aim of the book is to serve as a reference work for all those whose main interest is in the application of Fourier transform methods. These methods have found a wide variety of applications in the natural and technical sciences
Fourier transforms of distributions and their inverses; a collection of tables by
Fritz Oberhettinger(
Book
)
14 editions published between 1973 and 1980 in English and held by 556 WorldCat member libraries worldwide
14 editions published between 1973 and 1980 in English and held by 556 WorldCat member libraries worldwide
Fourier expansions; a collection of formulas by
Fritz Oberhettinger(
Book
)
20 editions published between 1973 and 2014 in English and held by 548 WorldCat member libraries worldwide
Fourier Expansions: A Collection of Formulas provides a collection of Fourier series. Its limited scope made a number of compromises necessary. The question regarding the choice and organization of the material to be included posed certain problems. In order to preserve some consistency it seemed best to stay within the framework of what one could call the ""classical"" Fourier series, i.e., those of the trigonometric and their simplest generalization the FourierBessel series
20 editions published between 1973 and 2014 in English and held by 548 WorldCat member libraries worldwide
Fourier Expansions: A Collection of Formulas provides a collection of Fourier series. Its limited scope made a number of compromises necessary. The question regarding the choice and organization of the material to be included posed certain problems. In order to preserve some consistency it seemed best to stay within the framework of what one could call the ""classical"" Fourier series, i.e., those of the trigonometric and their simplest generalization the FourierBessel series
Tables of Laplace transforms by
Fritz Oberhettinger(
Book
)
19 editions published between 1973 and 1980 in English and German and held by 479 WorldCat member libraries worldwide
This material represents a collection of integrals of the Laplace and inverse Laplace Transform type. The usef ness of this kind of information as a tool in various branches of Mathematics is firmly established. Previous publications include the contributions by A. Erdelyi and Roberts and Kaufmann (see References). Special consideration is given to results involving higher functions as integrand and it is believed that a substantial amount of them is presented here for the first time. Greek letters denote complex parameters within the given range of validity. Latin letters denote (unless otherwise stated) real positive parameters and a possible extension to complex values by analytic continuation will often pose no serious problem. The authors are indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manu script. Oregon State University Corvallis, Oregon Eastern Michigan University Ypsilanti, Michigan The Authors Contents Part I. Laplace Transforms In troduction. ... ... 1 1. 1 General Formulas. ... ... 3 1. 2 Algebraic Functions. ... ... 12 1. 3 Powers of Arbitrary Order. ... . 21 1. 4 Sectionally Rational and Rows of Delta Functions 28 1. 5 Exponential Functions. ... ... 37 1. 6 Logarithmic Functions. ... ... 48 1. 7 Trigonometric Functions. ... . 54 1. 8 Inverse Trigonometric Functions. ... 81 1. 9 Hyperbolic Functions. ... ... 84 1. 10 Inverse Hyperbolic Functions. ... . 99 1. 11 Orthogonal Polynomials .... ... 103 1. 12 Legendre Functions ... ... 113 1. 13 Bessel Functions of Order Zero and Unity ... 119 1. 14 Bessel Functions. ... ... 134 1. 15 Modified Bessel Functions
19 editions published between 1973 and 1980 in English and German and held by 479 WorldCat member libraries worldwide
This material represents a collection of integrals of the Laplace and inverse Laplace Transform type. The usef ness of this kind of information as a tool in various branches of Mathematics is firmly established. Previous publications include the contributions by A. Erdelyi and Roberts and Kaufmann (see References). Special consideration is given to results involving higher functions as integrand and it is believed that a substantial amount of them is presented here for the first time. Greek letters denote complex parameters within the given range of validity. Latin letters denote (unless otherwise stated) real positive parameters and a possible extension to complex values by analytic continuation will often pose no serious problem. The authors are indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manu script. Oregon State University Corvallis, Oregon Eastern Michigan University Ypsilanti, Michigan The Authors Contents Part I. Laplace Transforms In troduction. ... ... 1 1. 1 General Formulas. ... ... 3 1. 2 Algebraic Functions. ... ... 12 1. 3 Powers of Arbitrary Order. ... . 21 1. 4 Sectionally Rational and Rows of Delta Functions 28 1. 5 Exponential Functions. ... ... 37 1. 6 Logarithmic Functions. ... ... 48 1. 7 Trigonometric Functions. ... . 54 1. 8 Inverse Trigonometric Functions. ... 81 1. 9 Hyperbolic Functions. ... ... 84 1. 10 Inverse Hyperbolic Functions. ... . 99 1. 11 Orthogonal Polynomials .... ... 103 1. 12 Legendre Functions ... ... 113 1. 13 Bessel Functions of Order Zero and Unity ... 119 1. 14 Bessel Functions. ... ... 134 1. 15 Modified Bessel Functions
Tables of Bessel transforms by
Fritz Oberhettinger(
Book
)
18 editions published in 1972 in English and German and held by 470 WorldCat member libraries worldwide
This material represents a collection of integral tra forms involving Bessel (or related) functions as kernel. The following types of inversion formulas have been singled out. k I. g(y) = f (x) (xy) 2J (xy) dx J V 0 k I' . f (x) g (y) (xy) 2J (xy) dy J V 0 II. g(y) f(x) (XY)~K (xy)dx J v 0 c+ioo k 1 II'. f (x) = g (y) (xy) 2 [Iv (xy) + I_v(xy)]dy J 27fT cioo or also c+ioo k 1 II". f(x) = g (y) (xy) 2Iv (xy) dx J rri oo ci k III. g(y) f(x) (xy) 2y (xy) dx + J v 0 k III' . f(x) g(y) (xy) "1lv (xy) dy J 0 k IV. g(y) f (x) (xy) "Kv (xy) dx J 0 k g(y) (xy) 2Y (xy)dy IV'  f(x) J v 0 V Preface V. g(y) f(X)Kix(y)dx J 0 2 1 sinh (7TX) V'. f(x) 27T x g(y)y Kix(y)dy J 0 21~[r(~~+~~v)r(~~+~+~v)]1 VI. g(y) . J f (x) (xy) ~s (xy) dx o ~, v l~ 1 VI' . f(x) 2 [r (~~+~~v) r (~~+~+~v)]   J 5 (xy)]dy g(y) (XY)~[S~, v(xy) ~, v 0 [xy)~]dX VII. g(y) f(x)\ ~ J 0 0 VII'  f(x) g(y) \ [(xy) lz]dy ~ f 0 0 with \ (z) o (For notations and definitions see the appendix of this book.) The transform VII is also known as the divisor transform
18 editions published in 1972 in English and German and held by 470 WorldCat member libraries worldwide
This material represents a collection of integral tra forms involving Bessel (or related) functions as kernel. The following types of inversion formulas have been singled out. k I. g(y) = f (x) (xy) 2J (xy) dx J V 0 k I' . f (x) g (y) (xy) 2J (xy) dy J V 0 II. g(y) f(x) (XY)~K (xy)dx J v 0 c+ioo k 1 II'. f (x) = g (y) (xy) 2 [Iv (xy) + I_v(xy)]dy J 27fT cioo or also c+ioo k 1 II". f(x) = g (y) (xy) 2Iv (xy) dx J rri oo ci k III. g(y) f(x) (xy) 2y (xy) dx + J v 0 k III' . f(x) g(y) (xy) "1lv (xy) dy J 0 k IV. g(y) f (x) (xy) "Kv (xy) dx J 0 k g(y) (xy) 2Y (xy)dy IV'  f(x) J v 0 V Preface V. g(y) f(X)Kix(y)dx J 0 2 1 sinh (7TX) V'. f(x) 27T x g(y)y Kix(y)dy J 0 21~[r(~~+~~v)r(~~+~+~v)]1 VI. g(y) . J f (x) (xy) ~s (xy) dx o ~, v l~ 1 VI' . f(x) 2 [r (~~+~~v) r (~~+~+~v)]   J 5 (xy)]dy g(y) (XY)~[S~, v(xy) ~, v 0 [xy)~]dX VII. g(y) f(x)\ ~ J 0 0 VII'  f(x) g(y) \ [(xy) lz]dy ~ f 0 0 with \ (z) o (For notations and definitions see the appendix of this book.) The transform VII is also known as the divisor transform
Tables of Mellin transforms by
Fritz Oberhettinger(
Book
)
17 editions published in 1974 in English and German and held by 386 WorldCat member libraries worldwide
This book contains tables of integrals of the Mellin transform type zl J (a) 1> (z) q, (x)x dx o t Since the substitution x = e transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Parti cularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ø(z) corresponding to a given q, (x) by (a) is known, then ø(z) belonging to xaq, (x) or more general to P xaq, (x) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book.) A list of major contributions conce~ning Mellin trans forms is added at the end of the introduction. Latin letters (unless otherwise stated) denote real positive numbers while Greek letters denote complex parameters within the given range of validity. The author is indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manuscript. Oregon State University Corvallis, Oregon May 1974 Fritz Oberhettinger Contents Part I. Mellin Transforms Introduction. . .  .    .  ...     ...  .  . .    .  . 1 Some Applications of the Mellin Transform Analysis. . . . . . . ...  .  ... . ...  6 1. 1 General Formulas. ... 11 1. 2 Algebraic Functions and Powers of Arbitrary Order ... 13 1. 3 Exponential Functions.
17 editions published in 1974 in English and German and held by 386 WorldCat member libraries worldwide
This book contains tables of integrals of the Mellin transform type zl J (a) 1> (z) q, (x)x dx o t Since the substitution x = e transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Parti cularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ø(z) corresponding to a given q, (x) by (a) is known, then ø(z) belonging to xaq, (x) or more general to P xaq, (x) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book.) A list of major contributions conce~ning Mellin trans forms is added at the end of the introduction. Latin letters (unless otherwise stated) denote real positive numbers while Greek letters denote complex parameters within the given range of validity. The author is indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manuscript. Oregon State University Corvallis, Oregon May 1974 Fritz Oberhettinger Contents Part I. Mellin Transforms Introduction. . .  .    .  ...     ...  .  . .    .  . 1 Some Applications of the Mellin Transform Analysis. . . . . . . ...  .  ... . ...  6 1. 1 General Formulas. ... 11 1. 2 Algebraic Functions and Powers of Arbitrary Order ... 13 1. 3 Exponential Functions.
Formeln und Sätze für die speziellen Funktionen der mathematischen Physik by
Wilhelm Magnus(
Book
)
26 editions published between 1941 and 1948 in German and held by 324 WorldCat member libraries worldwide
26 editions published between 1941 and 1948 in German and held by 324 WorldCat member libraries worldwide
Anwendung der elliptischen Funktionen in Physik und Technik by
Fritz Oberhettinger(
Book
)
22 editions published between 1949 and 2013 in German and Undetermined and held by 317 WorldCat member libraries worldwide
22 editions published between 1949 and 2013 in German and Undetermined and held by 317 WorldCat member libraries worldwide
Formulas and theorems for the functions of mathematical physics by
Wilhelm Magnus(
Book
)
13 editions published between 1949 and 1954 in English and Undetermined and held by 143 WorldCat member libraries worldwide
13 editions published between 1949 and 1954 in English and Undetermined and held by 143 WorldCat member libraries worldwide
Higher transcendental functions by
Bateman Manuscript Project(
Book
)
6 editions published between 1953 and 1981 in English and Undetermined and held by 45 WorldCat member libraries worldwide
6 editions published between 1953 and 1981 in English and Undetermined and held by 45 WorldCat member libraries worldwide
Higher transcendental functions by
Harry Bateman(
Book
)
3 editions published in 1953 in Undetermined and English and held by 32 WorldCat member libraries worldwide
3 editions published in 1953 in Undetermined and English and held by 32 WorldCat member libraries worldwide
Formulas and theorems for the special functions of mathematical physics by
Wilhelm Magnus(
Book
)
1 edition published in 1966 in English and held by 25 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 25 WorldCat member libraries worldwide
Tables of integral transforms. Based, in part, on notes left by Harry Bateman by
Bateman Manuscript Project(
Book
)
3 editions published in 1954 in English and Hungarian and held by 16 WorldCat member libraries worldwide
3 editions published in 1954 in English and Hungarian and held by 16 WorldCat member libraries worldwide
Tables of Lebedev, Mehler, and generalized Mehler transforms by
Fritz Oberhettinger(
Book
)
1 edition published in 1961 in English and held by 11 WorldCat member libraries worldwide
INVERSION FORMULAS WITH KERNELS CONTAINING Bessel functions of purely imaginary order and Legendre functions of complex index with the real part1/2 (conical functions) as variable are presented as methods in solving certain boundary value problems of the wave or heat conduction equation involving wedge or conically shaped boundaries. Tables are appended for the vari us transforms. (Author)
1 edition published in 1961 in English and held by 11 WorldCat member libraries worldwide
INVERSION FORMULAS WITH KERNELS CONTAINING Bessel functions of purely imaginary order and Legendre functions of complex index with the real part1/2 (conical functions) as variable are presented as methods in solving certain boundary value problems of the wave or heat conduction equation involving wedge or conically shaped boundaries. Tables are appended for the vari us transforms. (Author)
Fourier Transforms of Distributions and Their Inverses by
Fritz Oberhettinger(
Book
)
10 editions published between 1973 and 2015 in English and Russian and held by 9 WorldCat member libraries worldwide
Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables
10 editions published between 1973 and 2015 in English and Russian and held by 9 WorldCat member libraries worldwide
Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables
Preobrazovanija Fur'e raspredelenij i ich obraščenija tablicy by
Fritz Oberhettinger(
Book
)
2 editions published in 1979 in Russian and Undetermined and held by 7 WorldCat member libraries worldwide
2 editions published in 1979 in Russian and Undetermined and held by 7 WorldCat member libraries worldwide
Formulas and theorems for the special functions of mathematical physics [by] Wilhelm Magnus, Fritz Oberhettinger [and] Raj
Pal Soni by
Wilhelm Magnus(
Book
)
1 edition published in 1966 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 5 WorldCat member libraries worldwide
Fourier expansions by
Fritz Oberhettinger(
)
3 editions published between 1973 and 2014 in English and Undetermined and held by 5 WorldCat member libraries worldwide
3 editions published between 1973 and 2014 in English and Undetermined and held by 5 WorldCat member libraries worldwide
Formulas and theorems for the special functions of mathematical physics by
Wilhelm Magnus(
Book
)
4 editions published between 1949 and 1966 in 3 languages and held by 4 WorldCat member libraries worldwide
4 editions published between 1949 and 1966 in 3 languages and held by 4 WorldCat member libraries worldwide
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Related Identities
 Magnus, Wilhelm 19071990 Author Editor
 Soni, Raj Pal
 Badii, Larry
 Erdélyi, Arthur Author Editor
 Bateman, Harry 18821946 Author
 Tricomi, F. G. (Francesco Giacomo) 1897 Editor
 Wermer, John Translator
 United States Office of Naval Research
 Bateman Manuscript Project
 Higgins, Theodore Parker 1920
Useful Links
Associated Subjects
Bessel functions Distribution (Probability theory) Elliptic functions Engineering mathematics Fourier analysis Fourier series Fourier transformations Functions Functions, Special Integral transforms Laplace transformation Mathematical physics Mathematics Mellin transform Physics Topological groups Transcendental functions Transformations (Mathematics)
Alternative Names
Fritz Oberhettinger deutscher Mathematiker
Fritz Oberhettinger Duits wiskundige (19111993)
Fritz Oberhettinger German mathematician
Fritz Oberhettinger tysk matematikar
Fritz Oberhettinger tysk matematiker
Oberchettinger, F.
Oberhettinger, F.
Oberhettinger, Fritz
Languages