Sentence examples for both hypergeometric functions and from inspiring English sources

They show how to construct exact solutions for the means in terms of both hypergeometric functions and Legendre functions.

We introduce some weighted hypergeometric functions and the suitable generalization of the Caputo fractional derivation.

Many researchers used various generalizations of the beta function to introduce new generalizations of hypergeometric functions and fractional operators.

The aim of this research is to provide many new hypergeometric transformations of Kampé de Fériet's double hypergeometric functions and Srivastava's triple hypergeometric functions, which are obtained with the help of the relations of Appell, Humbert, Horn and Srivastava's multiple hypergeometric functions.

Exact solutions were found in terms of hypergeometric functions, and a comparison of analytical and numerical results was shown.

Multi-variable hypergeometric functions and their reduction formulas have also been largely investigated (for example, see [3]).

with Φ denoting the confluent hypergeometric function and Gam denoting the complete Gamma function [31].

M ( a, b, x ) is the Kummer hypergeometric function and Γ denotes the gamma function.

Let be a weight function on, denotes the hypergeometric function, and denotes the Erdélyi-Kober type fractional left-sided integral.

Let be a weight function on, denotes the hypergeometric function, and denotes the Erdélyi-Kober type fractional right-sided integral.

where is the Gauss's hypergeometric function, and is the first type modified Bessel function of zero.