ACTA issues

On special Riemann xi function formulae of Hardy involving the digamma function

Alexander E. Patkowski

Acta Sci. Math. (Szeged) 87:1-2(2021), 107-114

Abstract. We consider some properties of integrals considered by Hardy and Koshliakov that have connections to the digamma function. We establish a new general integral formula that provides a connection to the polygamma function. We also obtain lower and upper bounds for Hardy's integral through properties of the digamma function.

DOI: 10.14232/actasm-020-664-3

AMS Subject Classification (1991): 11M06, 33C15

Keyword(s): Fourier integrals, Riemann xi function, digamma function

received 21.6.2020, revised 29.10.2020, accepted 2.11.2020. (Registered under 664/2020.)