Abstract
We answer a question of Berndt and Bowman, asking whether it is possible to deduce the value of the Ramanujan integral I from the value of the Ramanujan integral J, where
and
We also show that the second integral can be deduced from a classical expression of the ψ function due to Dirichlet and from the classical equality
which is a simple consequence of Frullani-Cauchy’s theorem.
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2000 Mathematics Subject ClassificationPrimary—33B15
Partially supported by MENESR, ACI NIM 154 Numération.
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Allouche, JP. Note on an integral of Ramanujan. Ramanujan J 14, 39–42 (2007). https://doi.org/10.1007/s11139-006-9003-7
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DOI: https://doi.org/10.1007/s11139-006-9003-7