The Laplace Transform of the Digamma Function: an Integral Due to Glasser, Manna and Oloa
نویسندگان
چکیده
The definite integral M(a) := 4 π ∫ π/2 0 x2 dx x2 + ln2(2e−a cosx) is related to the Laplace transform of the digamma function L(a) := ∫ ∞ 0 e−asψ(s+ 1) ds, by M(a) = L(a) + γ/a when a > ln 2. Certain analytic expressions for M(a) in the complementary range, 0 < a ≤ ln 2, are also provided.
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