On the q-derivative and q-series expansions

Zhi Guo Liu

doi:10.1142/S1793042113500759

On the q-derivative and q-series expansions

Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

Using a general q-series expansion, we derive some nontrivial q-formulas involving many infinite products. A multitude of Hecke-type series identities are derived. Some general formulas for sums of any number of squares are given. A new representation for the generating function for sums of three triangular numbers is derived, which is slightly different from that of Andrews, also implies the famous result of Gauss where every integer is the sum of three triangular numbers.

Original language	English
Pages (from-to)	2069-2089
Number of pages	21
Journal	International Journal of Number Theory
Volume	9
Issue number	8
DOIs	https://doi.org/10.1142/S1793042113500759
State	Published - Dec 2013

Keywords

Hecke-type series
q-Series
q-derivative
sums of squares

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10.1142/S1793042113500759

Cite this

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AB - Using a general q-series expansion, we derive some nontrivial q-formulas involving many infinite products. A multitude of Hecke-type series identities are derived. Some general formulas for sums of any number of squares are given. A new representation for the generating function for sums of three triangular numbers is derived, which is slightly different from that of Andrews, also implies the famous result of Gauss where every integer is the sum of three triangular numbers.

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KW - q-Series

KW - q-derivative

KW - sums of squares

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On the q-derivative and q-series expansions

Abstract

Keywords

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