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Series involving products of two E-functions

Published online by Cambridge University Press:  18 May 2009

Arun Verma
Arun Verma
Affiliation:
The UniversityLucknow, India
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In 1958 Ragab [3] deduced the sums of certain infinite series involving a product of two E-functions in terms of E-functions. MacRobert [2] gave a very simple alternative method for proving the results of Ragab. Later, Ragab [4, 5] in 1962 used a method similar to the one given by MacRobert to deduce a number of summations involving products of E-functions. In this paper, some more general summations of E-functions, which contain Ragab's results as special cases, are given. It may be mentioned that all the series summed run from n = – ∞ to + ∞co instead of n = 0 to + ∞.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 4 , July 1964 , pp. 172 - 176
Copyright
Copyright © Glasgow Mathematical Journal Trust 1964

References

REFERENCES

1.Bailey, W. N., Series of hypergeometric type which are infinite in both directions, Quart. J. Math. (Oxford) 7 (1936), 105–115.Google Scholar
2.MacRobert, T. M., Integration of E-functions with respect to their parameters, Proc. Glasgow Math. Assoc. 4 (1959), 84–87.CrossRefGoogle Scholar
3.Ragab, F. M., Expansions of an E-function in a series of products of E-functions, Proc. Glasgow Math. Assoc. 3 (1958), 194–195.CrossRefGoogle Scholar
4.Ragab, F. M., Summation of a series of products of E-functions, Proc. Glasgow Math. Assoc. 5 (1962), 118–120.CrossRefGoogle Scholar
5.Ragab, F. M., Reihen von Produkten MacRobertsche E-functionen, Math. Z. 78 (1962), 222–230.CrossRefGoogle Scholar