Identities involving special functions from hypergeometric solution of algebraic equations

Authors: JUAN LUIS GONZALEZ-SANTANDER

Abstract: From the algebraic solution of $x^{m}-x+t=0$ for $m=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these results, and applying other known reduction formulas of hypergeometric functions, we derive new reduction formulas of special functions as well as the calculation of some definite integrals in terms of elementary functions.

Keywords: Reduction formulas of special functions, hypergeometric functions, integrals of special functions, algebraic equations, trinomial equation

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