Hypergeometric functions are at the heart of many analytical and applied mathematical investigations. These functions, generally defined via power series that extend the geometric series, have been ...

The connection between functions of hypergeometric type and representations of certain Lie algebras is exploited by classifying the irreducible representations of the corresponding local Lie groups.

It is well known that the hypergeometric functions $_2F_1 (\alpha \pm 1, \beta, \gamma; t), _2F_1(\alpha, \beta \pm 1, \gamma; t), \quad _2F_1 (\alpha, \beta, \gamma \pm 1; t),$ which are continguous ...

Abstract: Hypergeometric functions occur in many shapes and flavours throughout mathematics and mathematical physics. The first such functions were introduced by Euler and studied in depth by Gauss.