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<p>Recently, Nath and Das investigated congruence properties for the second order mock theta function <i>B</i>(<i>q</i>). In their paper, they asked for analytic proofs of three identities on the second order mock theta functions <i>A</i>(<i>q</i>), <i>B</i>(<i>q</i>) and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu _2(q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>μ</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we settle Nath and Das’ open problem by using the (<i>p</i>,&#xa0;<i>k</i>)-parametrization of theta functions and several identities due to Hickerson and Mortenson.</p>

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Some identities on the second order mock theta functions

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Xingyuan Cai,
  • Eric H. Liu,
  • Olivia X. M. Yao

摘要

Recently, Nath and Das investigated congruence properties for the second order mock theta function B(q). In their paper, they asked for analytic proofs of three identities on the second order mock theta functions A(q), B(q) and \(\mu _2(q)\) μ 2 ( q ) . In this paper, we settle Nath and Das’ open problem by using the (p, k)-parametrization of theta functions and several identities due to Hickerson and Mortenson.