Abstract
Many important partial differential equations arising in the applications involve one or more parameters. A shifting relation for a problem involving such an equation permits expressing the solution corresponding to one value of a parameter in terms of a solution corresponding to a different value of this parameter. The Riemann–Liouville integral and its properties are employed to develop a set of shifting relations for solutions of a class of Cauchy problems involving an abstract version of the generalized hypergeometric equation. The results are applied to two examples, one of which involves the Riemann–Zeta function. They are also useful in developing properties of the hypergeometric functions.
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