Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

Some Fractional q-Integrals and q-Derivatives

Waleed A. Al-Salama1

a1 University of Alberta

A q-analogue of the integral ∣f(t)dt is defined by means of

S0013091500011469_eqn1

which is an inverse of the q–derivative

S0013091500011469_eqn2

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

S0013091500011469_eqn3

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

S0013091500011469_eqn4

(Received April 18 1966)

Footnotes

† Dedicated to the memory of my friend E. L. Whitney.