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Some Fractional q-Integrals and q-Derivatives†

Published online by Cambridge University Press:  20 January 2009

Waleed A. Al-Salam
Waleed A. Al-Salam
Affiliation:
University of Alberta
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A q-analogue of the integral ∣f(t)dt is defined by means of

which is an inverse of the q–derivative

The present author (2) has recently obtained a q–nalogue of a formula of Cauchy, namely,

where, for real or complex α and N a positive integer,

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 2 , December 1966 , pp. 135 - 140
Copyright
Copyright © Edinburgh Mathematical Society 1966

References

REFERENCES

(1) Agarwal, R. P., Associated basic hypergeometric series, Proc. Glasgow Math. Assoc. 1 (1952–1953), 182–184.CrossRefGoogle Scholar
(2) Al-Salam, W. A., q-analogues of Cauchy's formula, Proc. Amer. Math. Soc. 17 (1966), 616–621.Google Scholar
(3) Erdélyi, A. and Sneddon, I. N., Fractional integration and dual integral equations, Canad. J. Math. 14 (1962), 685–693.CrossRefGoogle Scholar
(4) Hahn, W., Uber die höheren Heineschen Reihen und eine einheitliche Theorie der sogenannten speziellen Funktionen, Math. Nachr. 3 (1950), 257–294.CrossRefGoogle Scholar
(5) Slater, L. J., Generalized Hypergeometric Functions (Cambridge University Press, 1966)Google Scholar