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pro vyhledávání: '"33B20"'
In this paper, we begin by applying the Laplace transform to derive closed forms for several challenging integrals that seem nearly impossible to evaluate. By utilizing the solution to the Pythagorean equation $a^2 + b^2 = c^2$, these closed forms be
Externí odkaz:
http://arxiv.org/abs/2405.14248
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution function, quant
Externí odkaz:
http://arxiv.org/abs/2405.11624
Autor:
Nemes, Gergő
Publikováno v:
SIGMA 20 (2024), 026, 14 pages
We study the resurgence properties of the coefficients $C_n(\tau)$ appearing in the asymptotic expansion of the incomplete gamma function within the transition region. Our findings reveal that the asymptotic behaviour of $C_n(\tau)$ as $n\to +\infty$
Externí odkaz:
http://arxiv.org/abs/2401.16671
Autor:
Sekatskii, S. K.
Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain new criteria equivalent to the Riemann hypothesis. Later, the same theorem was applied to calcula
Externí odkaz:
http://arxiv.org/abs/2403.09657
Autor:
Gaunt, Robert E.
The theory of normal variance mixture distributions is used to provide elementary derivations of closed-form expressions for the definite integrals $\int_0^\infty x^{-2\nu}\cos(bx)\gamma(\nu,\alpha x^2)\,\mathrm{d}x$ (for $\nu>1/2$, $b>0$ $\alpha>0$)
Externí odkaz:
http://arxiv.org/abs/2309.10004
Autor:
Pedersen, Henrik Laurberg
The asymptotic behaviour of the quantiles in the gamma distribution are investigated as the shape parameter tends to zero. Some remarks about the behaviour at infinity are given.
Comment: 16 pages. Revised version due to overlap with reference n
Comment: 16 pages. Revised version due to overlap with reference n
Externí odkaz:
http://arxiv.org/abs/2309.07234
First derivatives with respect to the parameters of the Whittaker function $\mathrm{W}_{\kappa ,\mu }\left( x\right) $ are calculated. Using the confluent hypergeometric function, these derivarives can be expressed as infinite sums of quotients of th
Externí odkaz:
http://arxiv.org/abs/2302.13830
First derivatives of the Whittaker function $\mathrm{M}_{\kappa ,\mu }\left(x\right) $ with respect to the parameters are calculated. Using the confluent hypergeometric function, these derivarives can be expressed as infinite sums of quotients of the
Externí odkaz:
http://arxiv.org/abs/2302.13776
Autor:
Cotti, Giordano
Publikováno v:
Journal de Math\'ematiques Pures et Appliqu\'ees, Volume 183, March 2024, Pages 102-136
In this paper, we address the integration problem of the isomonodromic system of quantum differential equations ($qDE$s) associated with the quantum cohomology of $\mathbb P^1$-bundles on Fano varieties. It is shown that bases of solutions of the $qD
Externí odkaz:
http://arxiv.org/abs/2210.05445
Autor:
Marichal, Jean-Luc, Zenaïdi, Naïm
Publikováno v:
Aequationes Mathematicae 98 (2) (2024) 455-481
In its additive version, Bohr-Mollerup's remarkable theorem states that the unique (up to an additive constant) convex solution $f(x)$ to the equation $\Delta f(x)=\ln x$ on the open half-line $(0,\infty)$ is the log-gamma function $f(x)=\ln\Gamma(x)
Externí odkaz:
http://arxiv.org/abs/2207.12694