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Tables of Bessel Transforms by Fritz Oberhettinger (English) Paperback Book
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- Sofort-KaufenTables of Bessel Transforms by Fritz Oberhettinger (English) Paperback Book
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Standort: Suwanee, Georgia, USA
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Artikelmerkmale
- Artikelzustand
- Book Title
- Tables of Bessel Transforms
- ISBN-13
- 9783540059974
- ISBN
- 9783540059974
Über dieses Produkt
Product Identifiers
Publisher
Springer Berlin / Heidelberg
ISBN-10
3540059970
ISBN-13
9783540059974
eBay Product ID (ePID)
150489291
Product Key Features
Number of Pages
X, 290 Pages
Publication Name
Tables of Bessel Transforms
Language
English
Publication Year
1972
Subject
Transformations, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Format
Trade Paperback
Dimensions
Item Weight
16.4 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
I. Hankel Transforms.- 1.1 General Formulas.- 1.2 Transforms of Order Zero.- 1.3 Transforms of Order Unity.- Transforms of General Order.- 1.4 Algebraic Functions and Powers with Arbitrary Index.- 1.5 Exponential and Logarithmic Functions.- 1.6 Trigonometric and Inverse Trigonometric Functions.- 1.7 Orthogonal Polynomials.- 1.8 Miscellaneous Functions.- 1.9 Legendre Functions.- 1.10 Bessel Functions of Argument x.- 1.11 Bessel Functions of Other Arguments.- 1.12 Modified Bessel Functions of Argument x.- 1.13 Modified Bessel Functions of Other Arguments.- 1.14 Functions Related to Bessel Functions.- 1.15 Parabolic Cylinder Functions.- 1.16 Whittaker Functions.- 1.17 Gauss' Hypergeometric Function.- II. Integral Transforms with Modified Bessel Functions as Kernel.- 2.1 General Formulas.- 2.2 Transforms of Order Zero.- Transforms of General Order.- 2.3 Elementary Functions.- 2.4 Higher Transcendental Functions.- III. Integral Transforms with Neumann Functions as Kernel.- 3.1 General Formulas.- 3.2 Transforms of Order Zero.- Transforms of General Order.- 3.3 Elementary Functions.- 3.4 Higher Transcendental Functions.- IV. Integral Transforms with Struve Functions as Kernel.- 4.1 General Formulas.- 4.2 Transforms of Order Zero.- 4.3 Elementary Functions.- 4.4 Higher Transcendental Functions.- V. Kontorovich-Lebedev Transforms.- VI. Transforms with Lommel Functions as Kernel.- VII. Divisor Transforms.- Appendix. List of Notations and Definitions.
Synopsis
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 c-ioo or also c+ioo k 1 II." f(x) = g (y) (xy) 2Iv (xy) dx J rri oo c-i 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., 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 c-ioo or also c+ioo k 1 II". f(x) = g (y) (xy) 2Iv (xy) dx J rri oo c-i 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., 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 c-ioo or also c+ioo k 1 II". f(x) = g (y) (xy) 2Iv (xy) dx J rri oo c-i 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.
LC Classification Number
QA299.6-433
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