Results 161 to 170 of about 39,153 (198)

Automorphic functions and Kummer's problem

Russian Mathematical Surveys, 1982
CONTENTS Introduction § 1. The work of Kubota and Patterson § 2. Results from analytic number theory § 3.
Venkov, Alexei, Proskurin, N.V.
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Kummer’s Tower and Big Zeta Functions

Journal of Mathematical Sciences, 2019
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Kummer-function representation of ridge traveling waves

Physical Review A, 1987
We present Kummer-function representation of an infinite set of local solutions for describing the double continua of two atomic electrons. Specific connection between the rate of flux loss from the ridge region and the double-excitation mechanism is discussed.
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Kummer's twenty-four functions and n-fractional calculus

Nonlinear Analysis: Theory, Methods & Applications, 1997
Summary: Many papers and books on fractional calculus have been reported by the author already. Kummer's twenty-four functions are the solutions to the homogeneous Gauss equations. In this paper, it is shown that the solutions of the Gauss equation obtained by an \(N\)-fractional calculus operator \(N^\nu\) method cover Kummer's twenty-four functions.
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Series of Bessel and Kummer-Type Functions

2017
This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the ...
Baricz, Árpád, Jankov Maširević, Dragana, Poganj, Tibor   +2 more
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Counting subwords in flattened involutions and Kummer functions

Journal of Difference Equations and Applications, 2016
In this paper, we consider the problem of counting subword patterns in flattened involutions, which extends recent work on set partitions. We determine generating function formulas for the distribution of τ on the set In of involutions of size n in all cases in which τ is a subword of length three.
Toufik Mansour, Mark Shattuck
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Certain arithmetic properties of coefficients of Kummer’s function

Journal of Mathematical Sciences, 2007
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Asymptotics for the Kummer function of Bose plasmas

Journal of Mathematical Physics, 1994
The asymptotic expansions for the Kummer function obtained in the study of the linear response of magnetized Bose plasmas at T=0 K are presented for large and small values of its parameter, thereby displaying the function’s asymptotic nonuniformity.
Kowalenko, Victor, Frankel, N. E.
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Automorphic Functions and the Kummer Problem

1990
In this chapter we acquaint the reader with the solution of the familiar number-theoretic problem of Kummer on the distribution of the arguments of Gauss cubic sums at primes of a corresponding field. This solution was obtained comparatively recently by Heath-Brown and Patterson, and here certain ideas and methods of the spectral theory of automorphic ...
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Kummer's formula for multiple gamma functions

2006
The multiple gamma function is defined as \(\Gamma_r(x)=\exp(\zeta'_r(0, x))\) where \[ \zeta_r(s, x)=\sum_{n_1,\dots,n_r=0}^\infty(n_1+\dots+n_r+x)^{-s} \] is the multiple Hurwitz zeta-function and the differentiation is in the first variable \(s\). Note that \(\Gamma_1(x)=\Gamma(x)/\sqrt{2\pi}\), where \(\Gamma(x)\) is the Euler gamma function. For \(
Kurokawa Nobushige, Koyama Shin-ya
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