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Transformations of some Gauss Hypergeometric Functions
, 2004
"... This paper presents explicit algebraic transformations of some Gauss hypergeometric functions. Specifically, the transformations considered apply to hypergeometric solutions of hypergeometric differential equations with the local exponent differences 1/k, 1/ℓ,1/m such that k, ℓ, m are positive integ ..."
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Cited by 12 (3 self)
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This paper presents explicit algebraic transformations of some Gauss hypergeometric functions. Specifically, the transformations considered apply to hypergeometric solutions of hypergeometric differential equations with the local exponent differences 1/k, 1/ℓ,1/m such that k, ℓ, m are positive
Hybrid GaussTrapezoidal Quadrature Rules
 SIAM Journal on Scientific Computing
, 1999
"... . A new class of quadrature rules for the integration of both regular and singular functions is constructed and analyzed. For each rule the quadrature weights are positive and the class includes rules of arbitrarily highorder convergence. The quadratures result from alterations to the trapezoidal r ..."
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Cited by 55 (1 self)
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. A new class of quadrature rules for the integration of both regular and singular functions is constructed and analyzed. For each rule the quadrature weights are positive and the class includes rules of arbitrarily highorder convergence. The quadratures result from alterations to the trapezoidal
Degenerate Gauss hypergeometric functions Kyushu
 J. Math
"... This paper studies terminating and illdefined Gauss hypergeometric functions. For their hypergeometric equations, the set of 24 Kummer’s solutions degenerates. We describe those solutions and relations between them. 1 ..."
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Cited by 8 (3 self)
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This paper studies terminating and illdefined Gauss hypergeometric functions. For their hypergeometric equations, the set of 24 Kummer’s solutions degenerates. We describe those solutions and relations between them. 1
Block Gauss and antiGauss quadrature with application to networks
 SIAM J. Matrix Anal. Appl
"... Abstract. Approximations of matrixvalued functions of the form WT f(A)W, where A ∈ Rm×m is symmetric, W ∈ Rm×k, with m large and k m, has orthonormal columns, and f is a function, can be computed by applying a few steps of the symmetric block Lanczos method to A with initial blockvector W ∈ Rm×k. ..."
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Cited by 3 (2 self)
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that under suitable conditions pairs of block Gauss and block antiGauss rules provide upper and lower bounds for the entries of the desired matrixvalued function. Extensions to matrixvalued functions of the form WT f(A)V, where A ∈ Rm×m may be nonsymmetric, and the matrices V,W ∈ Rm×k satisfy V TW = Ik
Transformations of algebraic Gauss hypergeometric functions
, 2003
"... A celebrated theorem of Klein implies that any hypergeometric differential equation with algebraic solutions is a pullback of one of the few standard hypergeometric equations with algebraic solutions. The most interesting cases are hypergeometric equations with tetrahedral, octahedral or icosahedra ..."
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Cited by 5 (2 self)
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or icosahedral monodromy groups. We give an algorithm for computing Klein’s pullback coverings in these cases, based on certain explicit expressions (Darboux evaluations) of algebraic hypergeometric functions. The explicit expressions can be computed from a data base (covering the Schwarz table) and using
AN ELEMENTARY APPROACH TO THE GAUSS HYPERGEOMETRIC FUNCTION
"... Abstract. We give an introduction to the Gauss hypergeometric function, the hypergeometric equation and their properties in an elementary way. Moreover we explicitly and uniformly describe the connection coefficients, the reducibility of the equation and the monodromy group of the solutions. 1. ..."
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Abstract. We give an introduction to the Gauss hypergeometric function, the hypergeometric equation and their properties in an elementary way. Moreover we explicitly and uniformly describe the connection coefficients, the reducibility of the equation and the monodromy group of the solutions. 1.
05 "Gauss"matrix GS
 IDENTITIES INVOLVING BINOMIALCOEFFICIENTS, . . .
, 2006
"... The matrix GS occurs as triangular scheme of coefficients, if the derivatives of the Gaussfunction are computed. This article is just a minor extension of the main subject (which covers binomial and related matrices) and is added here only because of the intriguing hierarchy of the matrixlogarit ..."
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The matrix GS occurs as triangular scheme of coefficients, if the derivatives of the Gaussfunction are computed. This article is just a minor extension of the main subject (which covers binomial and related matrices) and is added here only because of the intriguing hierarchy of the matrix
GaussHermite Approximation Formula
, 2004
"... A multidimesional function y(⃗r) defined by a sample of points {⃗ri,yi} is approximated by a differentiable function ˜y(⃗r). The problem is solved by using the GaussHermite folding method developed in the nuclear shell correction method by Strutinsky. 1 ..."
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A multidimesional function y(⃗r) defined by a sample of points {⃗ri,yi} is approximated by a differentiable function ˜y(⃗r). The problem is solved by using the GaussHermite folding method developed in the nuclear shell correction method by Strutinsky. 1
On the spectrum of Farey and Gauss maps
"... In this paper we introduce spaces of holomorphic functions given by generalized Borel and Laplace transforms which are left invariant by the transfer operators of the Farey map and its induced transformation, the Gauss map, respectively. ..."
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In this paper we introduce spaces of holomorphic functions given by generalized Borel and Laplace transforms which are left invariant by the transfer operators of the Farey map and its induced transformation, the Gauss map, respectively.
Representation of solutions of the Gauss
, 2008
"... hypergeometric equation by the multiple polylogarithms, functional relations of the multiple polylogarithms and relations of the multiple zeta values ..."
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hypergeometric equation by the multiple polylogarithms, functional relations of the multiple polylogarithms and relations of the multiple zeta values
Results 11  20
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