Some formulas for the Bernoulli and Euler polynomials at rational arguments

By Hari M. Srivastava. Mathematical Proceedings of the Cambridge Philosophical Society, 2000

217 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/61cff1eadb92e4d2147dea0dab0aec2e291ffc3b

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Citations in the corpus

Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler (2011, methodology): “Naturally, therefore, the corresponding constraints on |z| in the earlier investigations (see, for example, [45], [52], [53] and [66]) should also be modified accordingly.”
Integral and computational representations of the extended Hurwitz–Lerch zeta function (2011, methodology): “, [28,29,32]), fruitfully using the Hurwitz–Lerch Zeta function (z, s, a) and some of its above-mentioned generalizations, have motivated us to present here a further generalization and analogous investigation of a new family of Hurwitz–Lerch Zeta functions defined in the following form:”
Some expansion formulas for a class of generalized Hurwitz–Lerch Zeta functions (2006, methodology): “[7, 16, 17] and the references to the earlier works which are cited in each of these papers.”
A New Family of the λ -Generalized Hurwitz-Lerch Zeta Functions with Applications (2014, unknown): “11 (1)]; see also [26], [29, p.”
A new generalization of the Bernoulli and related polynomials (2010, background): “These so-called Apostol–Bernoulli polynomials Bn (x; λ) are defined by means of the following generating function (see [1, 19]):”
On the apostol-bernoulli polynomials (2004, methodology): “(4) By applying binomial series expansion and Leibniz’s rule, we first obtain the representation of the polynomials Bn(x, λ) involving the Gaussian hypergeometric functions, and thereout deduce Apostol’s formula (3); afterward we prove Theorem 3.”
Extensions of the Genocchi polynomials and their Fourier expansions and integral representations (2011, unknown): “…with G 2 n C 1 D 0 for n (cid:21) 1 and, for example, Some interesting analogues of the classical Bernoulli and Euler polynomials were investigated by Apostol ([2]), Luo and Srivastava ([9], [10], [11] and [15]), and these analogues are called the Apostol–Bernoulli and Apostol–Euler polynomials.”
Special functions related to Dedekind-type DC-sums and their applications (2009, background): “([2], [6], [16], [15], [14], [13], [24], [55], [56], [58], [29]) and see also the references cited in each of these earlier works.”
Some relationships between the generalized Apostol–Bernoulli polynomials and Hurwitz–Lerch Zeta functions (2006, methodology): “which was applied by Srivastava [5] in conjunction with Apostol’s formula [4, p.”
Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials (2005, methodology): “Moreover, both [9] and [10] were actually included in the list o citations at the end of Luo’s paper [6, p.”