Two q-summation formulas and q-analogues of series expansions for certain constants

TL;DR

This paper derives new q-summation formulas leading to series expansions involving the q-gamma function, enabling the creation of q-analogues for series expansions of specific mathematical constants.

Contribution

Introduces novel q-summation formulas and series expansions that serve as q-analogues of classical series for certain constants.

Findings

Derived new q-summation formulas

Established q-analogues of series expansions for constants

Connected q-series with the q-gamma function

Abstract

From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certain constants.