Geodesic
On integral equations involving Whittaker's function
Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 125-127

Voir la notice de l'article provenant de la source Cambridge University Press

Recently some inversion integrals for integral equations involving Legendre, Chebyshev, Gegenbauer and Laguerre polynomials in the kernel have been obtained [1, 2, 3, 5, 6]. In this note, two inversion integrals for integral equations involving Whittaker's function in the kernel are obtained. We shall make use of the following known integral [4, p. 402]The results of this note are based on the following two integrals, which are derived from (1) by writing u – t = (v – t)x.for m + 1 > 2v > – 1;for m + 1 > 2v > – 1. 
Srivastava, K. N. On integral equations involving Whittaker's function. Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 125-127. doi: 10.1017/S2040618500035309
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[1] 1.Buschman, R. G., An inversion integral for a Legendre transformation, Amer. Math. Monthly 69 (1962), 288–289. Google Scholar | DOI

[2] 2.Buschman, R. G., An inversion integral, Proc. Amer. Math. Soc. 13 (1962), 675–677. Google Scholar | DOI

[3] 3.Erdélyi, A., An integral equation involving Legendre's polynomial, Amer. Math. Monthly 70 (1963), 651–652. Google Scholar | DOI

[4] 4.Erdélyi, A., Tables of integral transforms, Vol. II (New York, 1954). Google Scholar

[5] 5.Li, Ta, A new class of integral transforms, Proc. Amer. Math. Soc. 11 (1960), 290–298. Google Scholar | DOI

[6] 6.Widder, D. V., The inversion of a convolution transform whose kernel is a Laguerre polynomial, Amer. Math. Monthly 70 (1963), 291–293. Google Scholar | DOI

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