<i>q</i>-Analogs of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">H</mi><mrow><mi mathvariant="bold-italic">n</mi><mo>,</mo><mi mathvariant="bold-italic">m</mi></mrow><mi mathvariant="bold-italic">r</mi></msubsup><mrow><mfenced open="(" close=")"><mi mathvariant="bold-italic">σ</mi></mfenced></mrow></mrow></semantics></math></inline-formula> and Their Applications

Abstract

In this paper, inspired by recent works, we define q-analogs of Hn,mσ and Hn,mrσ. By implementing them, we obtain new interesting results by taking the derivative or using generating functions.

Keywords

• alternative <i>q</i>-harmonic numbers
• <i>q</i>-polylogarithms
• generalized <i>q</i>-hyperharmonic numbers of order <i>r</i>