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On Sonine’s integral formula and its generalization. (English) Zbl 0040.03202


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[1] W. N. Bailey, On Hermite polynomials and associated Legendre functions, J. London Math. Soc. 14 (1939), 281 – 286. · Zbl 0026.31202 · doi:10.1112/jlms/s1-14.4.281
[2] T. J. I’a. Bromwich, An introduction to the theory of infinite series, Macmillan, 1926. · JFM 52.0208.05
[3] I. W. Busbridge, The evaluation of certain integrals involving products of Hermite polynomials, J. London Math. Soc. vol. 14 (1939) pp. 93-97. · Zbl 0021.12402
[4] G. A. Gibson, An elementary treatise on the calculus, Macmillan, 1922.
[5] Hsien-yü Hsü, Certain integrals and infinite series involving ultra-spherical polynomials and Bessel functions, Duke Math. J. 4 (1938), no. 2, 374 – 383. · Zbl 0019.06105 · doi:10.1215/S0012-7094-38-00429-6
[6] N. G. Shabde, On a definite integral involving Legendre functions, Proc. Benares Math. Soc. (N. S.) 5 (1943), 31 – 32. · Zbl 0063.06921
[7] G. Szegö, Über gewisse Potenzreihen mit lauter positiven Koeffizienten, Math. Zeit. vol. 37 (1932) pp. 674-688. · Zbl 0007.34401
[8] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge, 1922. · JFM 48.0412.02
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