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Evaluation of Triple Euler Sums
 ELECTRON. J. COMBIN
, 1996
"... Let a, b, c be positive integers and define the socalled triple, double and single Euler sums by #(a, b, c):= # # x=1 x1 # y=1 y1 # z=1 1 x a y b z c ,#(a, b):= # # x=1 x1 # y=1 1 x a y b and #(a):= # # x=1 1 x a . Extending earlier work about double sums, we pr ..."
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Cited by 11 (0 self)
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Let a, b, c be positive integers and define the socalled triple, double and single Euler sums by #(a, b, c):= # # x=1 x1 # y=1 y1 # z=1 1 x a y b z c ,#(a, b):= # # x=1 x1 # y=1 1 x a y b and #(a):= # # x=1 1 x a . Extending earlier work about double sums, we
On Stirling numbers and Euler sums
 J. Comput. Appl. Math
, 1997
"... Abstract. In this paper, we propose the another yet generalization of Stirling numbers of the rst kind for noninteger values of their arguments. We discuss the analytic representations of Stirling numbers through harmonic numbers, the generalized hypergeometric function and the logarithmic beta in ..."
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Cited by 14 (0 self)
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integral. We present then innite series involving Stirling numbers and demonstrate how they are related to Euler sums. Finally we derive the closed form for the multiple zeta function (p; 1; : : : ; 1) for p> 1. 1 Introduction and
On Stirling numbers and Euler sums
, 1996
"... In this paper, we propose the another yet generalization of Stirling numbers of the first kind for noninteger values of their arguments. We discuss the analytic representations of Stirling numbers through harmonic numbers, the generalized hypergeometric function and the logarithmic beta integral. W ..."
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. We present then infinite series involving Stirling numbers and demonstrate how they are related to Euler sums. Finally we derive the closed form for the multiple zeta function i(p; 1; : : : ; 1) for p? 1. 1 Introduction and notations. Throughout this article we will use the following definitions
Euler Sums and Contour Integral Representations
, 1998
"... This paper develops an approach to the evaluation of Euler sums that involve harmonic numbers, either linearly or nonlinearly. We give explicit formulæ for several classes of Euler sums in terms of Riemann zeta values. The approach is based on simple contour integral representations and residue comp ..."
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Cited by 44 (1 self)
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This paper develops an approach to the evaluation of Euler sums that involve harmonic numbers, either linearly or nonlinearly. We give explicit formulæ for several classes of Euler sums in terms of Riemann zeta values. The approach is based on simple contour integral representations and residue
Evaluation Of Triple Euler Sums
 Electron. J. Combin
, 1995
"... . Let a; b; c be positive integers and define the socalled triple, double and single Euler sums by i(a; b; c) := 1 X x=1 x\Gamma1 X y=1 y\Gamma1 X z=1 1 x a y b z c ; i(a; b) := 1 X x=1 x\Gamma1 X y=1 1 x a y b and i(a) := 1 X x=1 1 x a : Extending earlier work about double ..."
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. Let a; b; c be positive integers and define the socalled triple, double and single Euler sums by i(a; b; c) := 1 X x=1 x\Gamma1 X y=1 y\Gamma1 X z=1 1 x a y b z c ; i(a; b) := 1 X x=1 x\Gamma1 X y=1 1 x a y b and i(a) := 1 X x=1 1 x a : Extending earlier work about double
Parametric Euler sum identities
 J. Math. Anal. Appl
, 2005
"... Abstract. We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these sums. 1 ..."
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Cited by 8 (4 self)
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Abstract. We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these sums. 1
Evaluations of Some Variant Euler Sums
, 2006
"... In this note we present some elementary methods for the summation of certain Euler sums with terms involving 1 + 1/3 + 1/5 + · · · + 1/(2k − 1). ..."
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In this note we present some elementary methods for the summation of certain Euler sums with terms involving 1 + 1/3 + 1/5 + · · · + 1/(2k − 1).
Explicit evaluation of Euler sums
, 1994
"... In response to a letter from Goldbach, Euler considered sums of the form oe h (s; t) := 1 X n=1 (1 + 1 2 s + : : : + 1 (n \Gamma 1) s ) n \Gammat ; where s and t are positive integers. As Euler discovered by a process of extrapolation (from s + t 13), oe h (s; t) can be evaluated in te ..."
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In response to a letter from Goldbach, Euler considered sums of the form oe h (s; t) := 1 X n=1 (1 + 1 2 s + : : : + 1 (n \Gamma 1) s ) n \Gammat ; where s and t are positive integers. As Euler discovered by a process of extrapolation (from s + t 13), oe h (s; t) can be evaluated
Results 1  10
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584