2025/02/04 by Dixit, Atul, Sathyanarayana, Sumukha, Sharan, N. Guru
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #Primary 11F03 #Secondary 33B15
paper · doi:10.48550/arxiv.2502.02419
A two-term functional equation for an infinite series involving the digamma function and a logarithmic factor is derived. A modular relation on page 220 of Ramanujan's Lost Notebook as well as a corresponding recent result for the derivative of Deninger's function are two main ingredients in its derivation. An interesting integral \mathscrH(x), which is of independent interest, plays a prominent role in our functional equation. Several alternative representations for \mathscrH(x) are obtained.