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11: Bibliography V
  • G. Valent (1986) An integral transform involving Heun functions and a related eigenvalue problem. SIAM J. Math. Anal. 17 (3), pp. 688–703.
  • N. Ja. Vilenkin and A. U. Klimyk (1991) Representation of Lie Groups and Special Functions. Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms. Mathematics and its Applications (Soviet Series), Vol. 72, Kluwer Academic Publishers Group, Dordrecht.
  • N. Ja. Vilenkin and A. U. Klimyk (1993) Representation of Lie Groups and Special Functions. Volume 2: Class I Representations, Special Functions, and Integral Transforms. Mathematics and its Applications (Soviet Series), Vol. 74, Kluwer Academic Publishers Group, Dordrecht.
  • 12: 7.14 Integrals
    Fourier Transform
    Laplace Transforms
    Laplace Transforms
    7.14.7 0 e - a t C ( 2 t π ) d t = ( a 2 + 1 + a ) 1 2 2 a a 2 + 1 , a > 0 ,
    7.14.8 0 e - a t S ( 2 t π ) d t = ( a 2 + 1 - a ) 1 2 2 a a 2 + 1 , a > 0 .
    13: Bibliography E
  • A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1954a) Tables of Integral Transforms. Vol. I. McGraw-Hill Book Company, Inc., New York-Toronto-London.
  • A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1954b) Tables of Integral Transforms. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.
  • 14: 13.10 Integrals
    §13.10(ii) Laplace Transforms
    §13.10(iii) Mellin Transforms
    §13.10(iv) Fourier Transforms
    For integral transforms in terms of Whittaker functions see §13.23(iv). …
    15: 19.22 Quadratic Transformations
    Bartky’s Transformation
    Descending Gauss transformations include, as special cases, transformations of complete integrals into complete integrals; ascending Landen transformations do not. …
    16: Bibliography N
  • D. Naylor (1989) On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
  • G. Nemes (2013c) Generalization of Binet’s Gamma function formulas. Integral Transforms Spec. Funct. 24 (8), pp. 597–606.
  • 17: Bibliography P
  • E. Petropoulou (2000) Bounds for ratios of modified Bessel functions. Integral Transform. Spec. Funct. 9 (4), pp. 293–298.
  • A. Pinkus and S. Zafrany (1997) Fourier Series and Integral Transforms. Cambridge University Press, Cambridge.
  • A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev (1992a) Integrals and Series: Direct Laplace Transforms, Vol. 4. Gordon and Breach Science Publishers, New York.
  • A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev (1992b) Integrals and Series: Inverse Laplace Transforms, Vol. 5. Gordon and Breach Science Publishers, New York.
  • 18: Bibliography T
  • N. M. Temme (1985) Laplace type integrals: Transformation to standard form and uniform asymptotic expansions. Quart. Appl. Math. 43 (1), pp. 103–123.
  • I. Thompson (2012) A note on the real zeros of the incomplete gamma function. Integral Transforms Spec. Funct. 23 (6), pp. 445–453.
  • 19: Bibliography W
  • J. Wimp (1964) A class of integral transforms. Proc. Edinburgh Math. Soc. (2) 14, pp. 33–40.
  • R. Wong (1982) Quadrature formulas for oscillatory integral transforms. Numer. Math. 39 (3), pp. 351–360.
  • 20: Bibliography H
  • R. A. Handelsman and J. S. Lew (1971) Asymptotic expansion of a class of integral transforms with algebraically dominated kernels. J. Math. Anal. Appl. 35 (2), pp. 405–433.
  • P. Henrici (1977) Applied and Computational Complex Analysis. Vol. 2: Special Functions—Integral Transforms—Asymptotics—Continued Fractions. Wiley-Interscience [John Wiley & Sons], New York.