Series Associated with the Zeta and Related Functions

By Hari M. Srivastava, Junesang Choi. 2001

968 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/56c4a806bff7e7509bb50c8a6775c5e30014a5af

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Identities for the harmonic numbers and binomial coefficients (2011, background): “The book by Srivastava and Choi [ 23 ] also has many results associated with zeta and related functions.”
Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials (2005, background): “Moreover, both [9] and [10] were actually included in the list o citations at the end of Luo’s paper [6, p.”
Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials (2011, neutral): “ants ln(d i) with di 6= 1, the divisors of q, and logarithms of further algebraic numbers will occur. Theses are all transcendental numbers [50]. Let us list the ﬁrst few of these relations, see also [51] : − 1 2 γE +ψ 1 2 = ln(2) (5.9) − 1 3 γE +ψ 1 3 = 1 2 ln(3)+ π 18 √ 3 (5.10) − 1 3 γE +ψ”
A study of fractional integral operators involving a certain generalized multi‐index Mittag‐Leffler function (2018, background): “which leads us to the first assertion of Theorem 1 pertaining to the radius R of (absolute) convergence of the power series in (8) involving (17) and also to the assertion that the generalized multi-index Mittag-Leffler function E (αj ,βj )m[z] defined by (8) is an entire function in the complex z-p”
Special functions related to Dedekind-type DC-sums and their applications (2009, methodology): “In [58], Srivastava and Choi gave many applications of the Riemann zeta function, Hurwitz zeta function, Lerch zeta function, Dirichlet series for the polylogarithm function and Dirichlet’s eta function.”
Study on the q-analogue of a certain family of linear operators (2019, background): “We note that: (i) If q → 1− , then the function φq (s, b; z) reduces to the Hurwitz–Lerch zeta function and the operator J q,b coincides with the Srivastava–Attiya operator; we refer to [24, 25].”
$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series (2005, background): “In one of an impressive series of papers ( [4]; see also [54], Chapter 2), Barnes developed the so-called multiple zeta and multiple gamma functions.”
Series representations for some mathematical constants (2006, background): “Further series expansions as well as product and integral representations for the Catalan constant G can be found in (for example) [12,27], and [28, pp.”
A family of shifted harmonic sums (2015, background): “Many other evaluations are listed in the excellent book by Srivastava and Choi [24] (see also [25]).”