Results 31 to 40 of about 12,298,354 (363)
Inverses of Gamma Functions [PDF]
Constructive Approximation, 2014 Euler's Gamma function $ $ either increases or decreases on intervals between two consequtive critical points. The inverse of $ $ on intervals of increase is shown to have an extension to a Pick-function and similar results are given on the intervals of decrease, thereby answering a question by Uchiyama. The corresponding integral representations are
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Lens elliptic gamma function solution of the Yang–Baxter equation at roots of unity [PDF]
, 2017 We study the root of unity limit of the lens elliptic gamma function solution of the star-triangle relation, for an integrable model with continuous and discrete spin variables.
A. P. Kels, M. Yamazaki
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Relativistic Conic Beams and Spatial Distribution of Gamma-Ray Bursts [PDF]
, 2000 We study the statistics of gamma-ray bursts, assuming that gamma-ray bursts are cosmological and they are beamed in the form of a conical jet with a large bulk Lorentz factor $\sim 100$.
Heon‐Young Chang, Insu Yi, Renaud N.
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On the Multiple Gamma-Functions
Tokyo Journal of Mathematics, 1998 The authors obtain generalizations of the Shintani type infinite product representations for the \(r\)-ple gamma functions \(\Gamma_r(w;\widetilde\omega)\) and \(r\)-ple Stirling's modular forms \(\rho_r(\widetilde\omega)\) in the sense of Barnes. As an application, ``a simple proof'' of the inversion formulas of theta-function and Dedekind \(\eta ...
KATAYAMA, Koji, OHTSUKI, Makoto
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Recurrent identities for two special functions of hypergeometric type
Вестник Самарского университета: Естественнонаучная серия, 2023 The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral ...
Svetlana V. Podkletnova
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The density structure and star formation rate of non-isothermal polytropic turbulence [PDF]
, 2015 The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF).
Banerjee, Supratik, Federrath, Christoph
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Supercongruences for truncated hypergeometric series and p-adic gamma function [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2015 We prove three more general supercongruences between truncated hypergeometric series and p-adic gamma function from which some known supercongruences follow. A supercongruence conjectured by Rodriguez--Villegas and proved by E. Mortenson using the theory
Rupam Barman, N. Saikia
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Multiple Gamma Functions and Multiple $q$-Gamma Functions
Publications of the Research Institute for Mathematical Sciences, 1997 We give an asymptotic expansion ( the higher Stirling formula ) and an infinite product representation ( the Weierstrass canonical product representation ) of the Vigneras multiple gamma functions by considering the classical limit of the multiple q
Kimio Ueno, Michitomo Nishizawa
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On approximating the modified Bessel function of the second kind
Journal of Inequalities and Applications, 2017 In the article, we prove that the double inequalities π e − x 2 ( x + a ) < K 0 ( x ) < π e − x 2 ( x + b ) , 1 + 1 2 ( x + a ) < K 1 ( x ) K 0 ( x ) < 1 + 1 2 ( x + b ) $$ \frac{\sqrt{\pi}e^{-x}}{\sqrt{2(x+a)}}< K_{0}(x)< \frac{\sqrt{\pi }e^{-x}}{\sqrt ...
Zhen-Hang Yang, Yu-Ming Chu
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