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A note on the $l$-fold Bailey Lemma and Mixed Mock Modular forms

Alexander E. Patkowski

Abstract

In this paper we present a method for constructing multiple-sum $q$-series for what is known as Mixed Mock Modular forms. We also present some multi-sum analogues of the Durfee identity, and discuss a construction of its combinatorial interpretation in terms of partitions.

A note on the $l$-fold Bailey Lemma and Mixed Mock Modular forms

Abstract

In this paper we present a method for constructing multiple-sum -series for what is known as Mixed Mock Modular forms. We also present some multi-sum analogues of the Durfee identity, and discuss a construction of its combinatorial interpretation in terms of partitions.

Paper Structure

This paper contains 4 sections, 4 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. Observations on the $l$-fold Bailey Lemma
  3. Multi-sum $q$-series and mixed mock modular forms
  4. Multi-sum identities for products

Key Result

Theorem 2.1

If $(\alpha,\beta)$ is a $l$-fold Bailey pair relative to $a_j=a,$$j=1, 2, \cdots, l,$ then $(\bar{\alpha},\bar{\beta})$ is a $2l$-fold Bailey pair relative to $a_j=a$ where and

Theorems & Definitions (7)

  • Theorem 2.1
  • proof
  • Corollary 2.1.1
  • proof
  • Theorem 3.1
  • proof
  • Lemma 4.1