NEW ANALYSIS OF WITTAKER FUNCTIONS

Authors

  • S. F. RAGAB Mathematic Department, Faculty of Engineering, Cairo University. Egypt. A.R.E.

DOI:

https://doi.org/10.5556/j.tkjm.21.1990.4675

Keywords:

integrability of trigonometric series, delta-quasimonotone sequence

Abstract

Integrals involving products of two Whittaker functions and Bessel functions are evaluated in §§ 3,4. Also the integrals

\[ \int_0^\infty t^{\rho-1}W_{k_1m}(t)W_{-k_1m}(t)W_{\mu, \nu}\left(\frac{2iz}{t}\right)W_{\mu, \nu}\left(-\frac{2iz}{t}\right)\ dt\]

and

\[ \int_0^\infty t^{\rho-1}W_{k_1m}(t)W_{-k_1m}(t)W_{\mu, \nu}(2zt)W_{-\mu, \nu}(2zt)\ dt\]

are evaluated in § 5 while in § 6 integrals involving the product of three Whittaker functions are established.

References

T. M. MacRobert , "Functions of a Complex Variable" 4th edit. London (1954).

F. M. Ragab, Journal of the London Mathematical Society 37 (1962).

----, "Some formulae for the product of two Whittaker Functions", I( onimble Akademie Van Wetenschappen, Amsterdam Vol. (58), pp. 430-434, (1958).

F. M. Ragab , "Integrals involving products of Bessel functions", Annafi di Matematica V. LVI, pp. 301-312, (1961).

T. M. MacRobert, "Moltiplication formulae for the E functions", Pacifie journal of Math. Vol. 9, pp. 759-761, (1959).

F. M. Ragab, Proc. Glay, Math. Assoc. II, (1954).

T. M. MacRobert, Philos Magan Ser. 7. XXXI (1941).

F. M. Ragab, Proc. Glag. Math. Assoc i, (1951).

----, Proc. Glasgow. Math Assoc. II (1953).

----, Proc. Glasgow, Math. Ass. IL (1954).

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Published

1990-12-01

How to Cite

RAGAB, S. F. (1990). NEW ANALYSIS OF WITTAKER FUNCTIONS. Tamkang Journal of Mathematics, 21(4), 303–326. https://doi.org/10.5556/j.tkjm.21.1990.4675

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