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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.)
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