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Explicit evaluations of extended Euler sums [PDF]
, 2006 In this paper, we consider two types of extended Euler sums:Ep,q(k)=∑n=1∞1nq∑r=1kn1rp,Tp,q(k)=∑n=1∞1nq∑r=1⌊n/k⌋1rp,where ⌊x⌋ is the largest integer ⩽x. In particular, Ep,q(1)=Tp,q(1) are classical Euler sums.
Eie, Minking, Chen, Kwang-Wu
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EXTENSIONS OF EULER-TYPE SUMS AND RAMANUJAN-TYPE SUMS
Kyushu Journal of Mathematics, 2021 We define a new kind of classical digamma function, and establish its some fundamental identities. Then we apply the formulas obtained, and extend tools developed by Flajolet and Salvy to study more general Euler type sums. The main results of Flajolet and Salvy's paper \cite{FS1998} are the immediate corollaries of main results in this paper ...
openaire +3 more sources
Families of Integrals of Polylogarithmic Functions
Mathematics, 2019 We give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing ...
Anthony Sofo
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Relationship between alternating sums of powers of integers and sums of powers of integers [PDF]
Notes on Number Theory and Discrete MathematicsIn this note, we consider the alternating sums of powers of integers. We write alternating sum of powers of integers as the linear combination of sums of powers of integers. As the coefficients, the special value of the Euler polynomial appears.
Minoru Yamamoto
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Mathematics, 2021 This work presents an overview of the summability of divergent series and fractional finite sums, including their connections. Several summation methods listed, including the smoothed sum, permit obtaining an algebraic constant related to a divergent ...
Jocemar Q. Chagas +2 more
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Identities of Symmetry for Higher-Order Generalized q-Euler Polynomials
Abstract and Applied Analysis, 2014 We investigate the properties of symmetry in two variables related to multiple Euler q-l-function which interpolates higher-order q-Euler polynomials at negative integers.
D. V. Dolgy +3 more
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Sums of finite products of Legendre and Laguerre polynomials
Advances in Difference Equations, 2018 In this paper, we study sums of finite products of Legendre and Laguerre polynomials and derive Fourier series expansions of functions associated with them.
Taekyun Kim +3 more
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Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions,
Daeyeoul Kim, Yilmaz Simsek
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Some results on q-harmonic number sums
Advances in Difference Equations, 2018 In this paper, we establish some relations involving q-Euler type sums, q-harmonic numbers and q-polylogarithms. Then, using the relations obtained with the help of q-analog of partial fraction decomposition formula, we develop new closed form ...
Xin Si
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Proceedings of the 3rd International Workshop on Euler Diagrams (Euler Diagrams 2012) [PDF]
, 2012 The 3rd International Workshop on Euler Diagrams (Euler Diagrams 2012) was held in Canterbury, UK on 2nd July 2012 in conjunction with the 7th International Conference on the Theory and Application of Diagrams (Diagrams 2012). Euler diagrams represent
Micallef, Luana
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