Hostname: page-component-7dd5485656-6kn8j Total loading time: 0 Render date: 2025-10-31T01:01:34.840Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Information

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