Ramanujan–Fine integrals for level 10

Authors

Shaun Cooper
Timothy Huber, The University of Texas Rio Grande ValleyFollow
Jeffery Opoku

Document Type

Article

Publication Date

1-28-2025

Abstract

We investigate the question of when an eta quotient is a derivative of a formal power series with integer coefficients and present an analysis in the case of level 10. As a consequence, we establish and classify an infinite number of integral evaluations such as

∫e−2π/10√0q∏j=1∞(1−qj)3(1−q10j)8(1−q5j)7dq=14(10−45–√−−−−−−−−√−1). We describe how the results were found and give reasons for why it is reasonable to conjecture that the list is complete for level 10.

Comments

Original published version available at https://doi.org/10.1007/s11139-024-00995-3

https://rdcu.be/d82UG

Recommended Citation

Cooper, Shaun, Timothy Huber, and Jeffery Opoku. "Ramanujan–Fine integrals for level 10." The Ramanujan Journal 66, no. 2 (2025): 1-28. https://doi.org/10.1007/s11139-024-00995-3

Publication Title

The Ramanujan Journal

DOI

10.1007/s11139-024-00995-3