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MOMENTS OF A RANDOM VARIABLE ARISING FROM LAPLACIAN RANDOM VARIABLE
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초록
Let X be the Laplacian random variable with parameters (a, b) = (0, 1), and let (Xⱼ)ⱼ≥1 be a sequence of mutually independent copies of X. In this note, we explicitly determine the moments of the random variable ∑ₖ₌₁^∞ (Xₖ / 2kπ) in terms of the Bernoulli and Euler numbers.
Abstract
Let X be the Laplacian random variable with parameters (a, b) = (0, 1), and let (Xⱼ)ⱼ≥1 be a sequence of mutually independent copies of X. In this note, we explicitly determine the moments of the random variable ∑ₖ₌₁^∞ (Xₖ / 2kπ) in terms of the Bernoulli and Euler numbers.
참고문헌 (7)
- Abramowitz, M., "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables" (1972)
- Ciaurri, O, "Euler’s product expansion for the sine: an elementary proof", Amer. Math. Monthly, 122(7), pp.693~695 (2015)
- Kim, T., "Euler numbers and polynomials associated with zeta functions", Abstr. Appl. Anal (2008)
- Kim, T, "Probabilistic Bernoulli and Euler polynomials", Russ. J. Math. Phys, 31(1), pp.94~105 (2024)
- Papoulis, A., "Probability, random variables, and stochastic processes" (1984), McGraw-Hill
- Srivastava, H. M, "Remarks on some relationships between the Bernoulli and Euler polynomials", Appl. Math. Lett, 17, pp.375~380 (2004)
- "Laplace Distribution"[URL]
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