Expansion formulas for multiple basic hypergeometric series over root systems

Gaurav Bhatnagar; Surbhi Rai

Expansion formulas for multiple basic hypergeometric series over root systems

Classical Analysis and ODEs 2022-02-22 v2

Authors: Gaurav Bhatnagar , Surbhi Rai

Abstract

We extend expansion formulas of Liu given in 2013 to the context of multiple series over root systems. Liu and others have shown the usefulness of these formulas in Special Functions and number-theoretic contexts. We extend Wang and Ma's generalizations of Liu's work which they obtained using $q$ -Lagrange inversion. We use the $A_n$ and $C_n$ Bailey transformation and other summation theorems due to Gustafson, Milne, Milne and Lilly, and others, from the theory of $A_n$ , $C_n$ and $D_n$ basic hypergeometric series.

Keywords

hypergeometric functions special functions and series expansions extension theorems

Cite

@article{arxiv.2109.02827,
  title  = {Expansion formulas for multiple basic hypergeometric series over root systems},
  author = {Gaurav Bhatnagar and Surbhi Rai},
  journal= {arXiv preprint arXiv:2109.02827},
  year   = {2022}
}

Comments

Final accepted version (to appear) in Adv. Appl. Math. Minor changes as suggested by referees were made

Expansion formulas for multiple basic hypergeometric series over root systems

Abstract

Keywords

Cite

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