Hjalmar Mellin names a multiplicative version of the “two-sided” form of this operation. For 10 points each:
[10h] Name this operation that may be thought of as the continuous analogue of a power series. Mellin derived a formula for the inverse of this operation that takes the limit of an integral over a vertical contour.
ANSWER: Laplace transform [accept inverse Laplace transform]
[10e] This function of negative s times t is the kernel of the Laplace transform. The Euler-Mascheroni constant appears when taking the Laplace transform of this function’s inverse, the natural logarithm.
ANSWER: exponential function [or e to the x; accept anything indicating that e is being raised to a power; accept negative exponential]
[10m] The Euler–Mascheroni constant is denoted by this letter. Applying the Laplace transform to a power generates a function denoted by the uppercase version of this letter that has poles at the nonpositive integers.
ANSWER: gamma
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