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A Basic Analogue of MacRobert's E-Function

Published online by Cambridge University Press:  18 May 2009

R. P. Agarwal
R. P. Agarwal
Affiliation:
Lucknow University, India
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MacRobert [2] in 1937 defined the E-function as

where the symbol denotes that to the expression following it, a similar expression with α and β interchanged is to be added. For (1) he also gave the integral representation

where Re β > 0, | arg z | < π.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 1 , January 1961 , pp. 4 - 7
Copyright
Copyright © Glasgow Mathematical Journal Trust 1961

References

1.Hahn, W., Über die höheren Heineschen Reihenund eine einheitliche Theorie der sogenannten speziellen Funktionen, Math. Nachr., 3 (1950), 257–294.CrossRefGoogle Scholar
2.MacRobert, T. M., Induction proofs of the relations between certain asymptotic expansions and corresponding generalised hypergeometric series, Proc. Roy. Soc. Edinburgh 58 (1937), 1–13.Google Scholar
3.Watson, G. N., The continuations of functions defined by generalised hypergeometric series, Trans. Cambridge Phil. Soc. 21 (1909), 281–299.Google Scholar