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2013•International Journal of Number TheoryRequires access

ON THE q-DERIVATIVE AND q-SERIES EXPANSIONS

Zhi-Guo Liu

Open publisher page 43 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.

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What this paper is about

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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OpenAlex reports 43 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Mathematics, Series (stratigraphy), Integer (computer science), Gauss, Generating function, Representation (politics), Gauss sum, Function (biology)

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