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Summation of a series of products of E-functions

Published online by Cambridge University Press:  18 May 2009

F. M. Ragab
F. M. Ragab
Affiliation:
Cairo University, Cairo
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In previous papers [1, 2, 3] the sums of a number of series of products of E-functions have been found. For the definitions and properties of the E-functions the reader is referred to [4, pp. 348–358]. In § 3 a further series of this type is given. The proof is based on an integral of an E-function with respect to its parameters, to be established in § 2. Similar integrals were given in [5] and [6].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 3 , January 1962 , pp. 118 - 120
Copyright
Copyright © Glasgow Mathematical Journal Trust 1962

References

1.Ragab, F. M., Expansion of an E-function in a series of products of E-functions, Proc. Glasgow Math. Assoc. 3 (1958), 194–195.CrossRefGoogle Scholar
2.Ragab, F. M., Expansions for products of two Whittaker functions, Div. Electromag. Res., Inst. Math. Sci., New York Univ., Res. Rep. No. BR–23 (1957).Google Scholar
3.Ragab, F. M., An expansion involving confluent hypergeometric functions, Nieuw Arch. Wisk. (3) 6 (1958), 52–54.Google Scholar
4.MacRobert, T. M., Functions of a complex variable, 4th edn. (London, 1954).Google Scholar
5.Ragab, F. M., Integration of E-functions and related functions with respect to their parameters, Nederl. Akad. Wetensch. Proc. Ser. A 61 (1958), 335–340.CrossRefGoogle Scholar
6.Ragab, F. M., Integration of E-functions with regard to their parameters, Proc. Glasgow Math. Assoc. 3 (1957), 94–98.CrossRefGoogle Scholar
7.Bailey, W. N., Generalized hypergeometric series (Cambridge, 1935).Google Scholar