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Some Fractional q-Integrals and q-Derivatives†

  • Waleed A. Al-Salam (a1)
Extract

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,

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COPYRIGHT: © Edinburgh Mathematical Society 1966
References
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(1) Agarwal, R. P., Associated basic hypergeometric series, Proc. Glasgow Math. Assoc. 1 (1952–1953), 182–184.
(2) Al-Salam, W. A., q-analogues of Cauchy's formula, Proc. Amer. Math. Soc. 17 (1966), 616–621.
(3) Erdélyi, A. and Sneddon, I. N., Fractional integration and dual integral equations, Canad. J. Math. 14 (1962), 685–693.
(4) Hahn, W., Uber die höheren Heineschen Reihen und eine einheitliche Theorie der sogenannten speziellen Funktionen, Math. Nachr. 3 (1950), 257–294.
(5) Slater, L. J., Generalized Hypergeometric Functions (Cambridge University Press, 1966)
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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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