Laplace transform - 2024 PLAYTIME @ Harvard

Question

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

<JC, Other Science - Math>

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Summary


2025 PLAYTIME @ CWRU	12/10/2024	Y	5	10.00	80%	20%	0%
2025 PLAYTIME @ Claremont	12/10/2024	Y	5	16.00	100%	60%	0%
2025 PLAYTIME @ Florida	12/10/2024	Y	2	15.00	100%	50%	0%
2025 PLAYTIME @ Florida	12/10/2024	Y	1	10.00	100%	0%	0%
2024 PLAYTIME @ Harvard	04/26/2025	Y	4	12.50	75%	25%	25%
2024 PLAYTIME @ JHU	10/26/2024	Y	8	12.50	88%	38%	0%
2025 PLAYTIME @ Northwest	12/10/2024	Y	4	17.50	75%	75%	25%
2025 PLAYTIME Online	04/26/2025	Y	9	15.56	100%	56%	0%
2025 PLAYTIME @ Sheffield	12/10/2024	Y	6	15.00	100%	50%	0%
2025 PLAYTIME @ Sheffield	12/10/2024	Y	1	30.00	100%	100%	100%
2024 PLAYTIME @ Virginia Tech	07/11/2025	Y	3	16.67	100%	67%	0%

Data


Lexington	BU	0	0	0	0
MIT	Brown	0	10	0	10
Belmont	Harvard	0	10	0	10
RIT	Brandeis	10	10	10	30