Evaluating a logarithmic Fresnel integral by differentiating under the integral sign
Differentiating the Mellin transform of the sine function with respect to its exponent evaluates a logarithmic Fresnel-type integral in terms of Euler's constant.
A mathematics notebook
Tagged: mellin-transform
Notes on integrals, infinite series, and number theory.
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Mellin transforms of sine and cosine via a quarter-circle contour
Rotating the positive real axis to the positive imaginary axis via an indented quarter-circle contour evaluates the Mellin transforms of sine and cosine.
Ramanujan's Master Theorem: Part I
Use Ramanujan's master theorem to connect power-series coefficients with Mellin transforms of Bessel functions.