TABLES OF INTEGRAL TRANSFORMS. Volume II. Based, in Part, on Notes Left by Harry Bateman Late Professor of Mathematics, Theoretical Physics, and Aeronautics at the California Institute of Technology.

PREFACE......Page 8
STANDARD FORMS......Page 10
CONTENTS......Page 12
BESSEL TRANSFORMS......Page 16
CHAPTER VIII. HANKEL TRANSFORMS......Page 18
8.1 General formulas......Page 20
8.2 Hankel transforms of order zero, Elementary functions......Page 22
8.3Hankel transforms of order zero, Higher transcendental functions......Page 28
8.4 Hankel transforms of order unity......Page 33
8.5 Algebraic functions and powers with arbitrary index......Page 36
8.6 Exponential and logarithmic functions......Page 43
8.7 Trigonometric and inverse trigonometric functions......Page 47
8.8 Hyperbolic and inverse hyperbolic functions......Page 56
8.9 Orthogonal Polynomials......Page 57
8.10 Legendre Functions......Page 59
8.11 Bessel functions of argument kx......Page 62
8.12 Bessel functions of other arguments......Page 71
8.13 Modified Bessel functions of argument kx......Page 78
8.14 Modified Bessel functions of other arguments......Page 82
8.15 Functions related to Bessel functions......Page 87
8.16 Parabolic cylinder functions......Page 91
8.17 Gauss' hypergeometric function......Page 95
8.18 Confluent hypergeometric functions......Page 97
8.19 Generalized hypergeometric series and miscellaneous functions......Page 102
CHAPTER IX. Y-TRANSFORMS......Page 108
9.1. General formulas......Page 110
9.2. Algebraic functions and powers with an arbitrary index......Page 111
9.3. Other elementary functions......Page 120
9.4. Higher transcendental functions......Page 123
CHAPTER X. K - TRANSFORMS......Page 136
10.1. General formulas......Page 140
10.2. Elementary functions......Page 142
10.3, Higher transcendental functions......Page 149
CHAPTER XI. H - TRANSFORMS......Page 170
11.1. General formulas......Page 172
11.2. Elementary functions......Page 173
11.3, Higher transcendental functions......Page 177
CHAPTER XI1. KONTOROVICH - LEBEDEV TRANSFORMS......Page 188
12.1. Formulas......Page 190
MISCELLANEOUS TRANSFORMS......Page 194
CHAPTER XI11. FRACTIONAL INTEGRALS......Page 196
13.1. Riemann-Liouville fractional integrals......Page 200
13.2. Weyl fractional integrals......Page 216
CHAPTER XIV. STIELTJES TRANSFORMS......Page 228
14.1 General formulas......Page 230
14.2 Elementary functions......Page 231
14.3 Higher transcendental functions......Page 239
14.4 Generalized Stieltjes transforms......Page 248
CHAPTER XV. HILBERT TRANSFORMS......Page 254
15.2 Elementary functions......Page 258
15.3 Higher transcendental functions......Page 268
INTEGRALS OF HIGHER TRANSCENDENTAL FUNCTIONS......Page 278
CHAPTER XVI. ORTHOGONAL POLYNOMIALS......Page 280
16.1 Tchebichef polynomials......Page 286
16.2 Legendre polynomials.......Page 291
16.3 Gegenbauer polynomials......Page 295
16.4 Jacobi polynomials......Page 299
16.5 Hermite polynomials......Page 303
16.6 Laguerre polynomials......Page 307
CHAPTER XVII. GAMMA FUNCTION, INCOMPLETE GAMMA FUNCTIONS AND RELATED FUNCTIONS......Page 310
17.1 The gamma function......Page 312
17.2 The Psi function......Page 320
17.3 Incomplete gamma functions and related functions......Page 321
CHAPTER XVIII. LEGENDRE FUNCTIONS......Page 326
18.1 Legendre functions of variable ax+b: finite intervals......Page 328
18.2 Legendre functions of variable ax+b: infinite intervals......Page 335
18.3 Legendre functions of other variables......Page 341
CHAPTER XX. BESSEL FUNCTIONS......Page 346
19.1 Bessel functions of argument x. Finite intervals......Page 348
19.2 Bessel functions of argument X , Infinite intervals......Page 354
19.3 Bessel functions of arguments ax+b, x(2), x(-1)......Page 364
19.4 Bessel functions of other arguments......Page 373
19.5 Modified Bessel functions of argument x......Page 379
19.6 Modified Bessel functions of other arguments......Page 387
19.7 Bessel functions and modified Bessel functions of variable order......Page 394
19.8 Functions related to Bessel functions......Page 398
CHAPTER XX. HYPERGEOMETRIC FUNCTIONS......Page 406
20.1 Parabolic cylinder functions g......Page 410
20.2 Gauss' hypergeometric series......Page 413
20.3 Confluent hypergeometric functions......Page 416
20.4 MacRobert's E-function......Page 429
20.5 Meijer's G-function......Page 432
APPENDIX. Notations and definitions of higher transcendental functions......Page 438
INDEX OF NOTATIONS......Page 464