On second order mock theta function $ B(q) $

Harman Kaur; Meenakshi Rana; Harman Kaur; Meenakshi Rana

doi:10.3934/era.2022003

Electronic Research Archive

2022, Volume 30, Issue 1: 52-65. doi: 10.3934/era.2022003

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Research article

On second order mock theta function $ B(q) $

Harman Kaur ^,,
Meenakshi Rana ^,

School of Mathematics, Thapar Institute of Engineering and Technology, Patiala-147004, India

Received: 20 October 2021 Revised: 23 November 2021 Accepted: 23 November 2021 Published: 09 December 2021

In this paper, we present some arithmetic properties for the second order mock theta function $ B(q) $ given by McIntosh as:

$ B(q) = \sum\limits_{n = 0}^{\infty}\frac{q^n(-q;q^2)_n}{(q;q^2)_{n+1}}. $
- mock theta function,
- congruences
Citation: Harman Kaur, Meenakshi Rana. On second order mock theta function $ B(q) $[J]. Electronic Research Archive, 2022, 30(1): 52-65. doi: 10.3934/era.2022003

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Abstract

In this paper, we present some arithmetic properties for the second order mock theta function $ B(q) $ given by McIntosh as:

$ B(q) = \sum\limits_{n = 0}^{\infty}\frac{q^n(-q;q^2)_n}{(q;q^2)_{n+1}}. $

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