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On the squares of Weber's parabolic cylinder functions and certain integrals connected with them

Published online by Cambridge University Press:  20 January 2009

S. C. Mitra
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The parabolic cylinder functions Dn(x) and D−(n+1) (± ix) are defined by

for all values of n and x.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 1 , March 1934 , pp. 27 - 32
Copyright
Copyright © Edinburgh Mathematical Society 1934

References

page 27 note 1 Whittaker, and Watson, , Modern Analysis (third edition), 347–49.Google Scholar

page 28 note 1 Appell, Comptes Rendus, 91. The method had been previously used by Heine in a similar problem relating to P m(x) P n (x). See the Appendix to Heine's Theorie der Kiigelfunhtionen (1878 edition).Google Scholar

My attention to this reference was drawn by a referee who kindly suggested some improvements also.

page 29 note 1 Proc. London Math. Soc. (2), 17 (1919), 116–48, 8 (1910), 416. See also a paper by Adamoff in Ann. de l'lnstitut Polytechnique de St Petersbourg, 5 (1906), 127–43.Google Scholar

page 30 note 1 Proc. London Math. Soc. (2), 34 (1932), 118. See also (2), 8 (1908), 397–400.Google Scholar

page 31 note 1 CfBromwich, Theory of Infinite Series. §176.Google Scholar

page 31 note 2 loc. cit., 116.Google Scholar

page 32 note 1 Bull Calcutta Math. Soc., 17, 34.Google Scholar