Geodesic
The use of a connection between integral transforms for the computation of integrals
Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 129-137 
V. S. Ryko. The use of a connection between integral transforms for the computation of integrals. Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 129-137. http://geodesic.mathdoc.fr/item/MZM_1974_15_1_a13/
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     title = {The use of a~connection between integral transforms for the computation of integrals},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_1_a13/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A theorem is proved which establishes a connection between four well-known integral transforms: Laplace, Kantorovich–Lebedev, Mehler–Fok, and the $K$-transform of Meier. This theorem is used to calculate a number of integrals containing the Legendre function $\beta_{\frac12+i\tau}(x)$, and also the MacDonald function $K_{i\tau}$. Certain other integrals can be calculated by using the indicated method.