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A New Formula for the Bernoulli Polynomials
Results in Mathematics, 2010The author defines \(r\)-Whitney numbers \(w_{m,r}(n,k)\) and \(W_{m,r}(n,k)\) of the first and second kind by the equalities \[ m^nx^{\underline{n}}=\sum_{k=0}^nw_{m,r}(n,k)(mx+r)^k \] and \[ (mx+r)^n=\sum_{k=0}^nm^kW_{m,r}(n,k)x^{\underline{k}} \] with \(x^{\underline{n}}=x(x-1)\cdots(x-n+1)\) denoting falling factorials. These numbers are also given
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Formulas for Bernoulli Numbers and Polynomials
Results in MathematicsSpecial polynomials and numbers possess much importance in multifarious areas of sciences such as physics, mathematics, applied sciences, engineering, and other related research fields covering differential equations, number theory, functional analysis, quantum mechanics, mathematical analysis, mathematical physics, and so on.
Ulrich Abel, Horst Alzer
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p-Bernoulli and geometric polynomials
International Journal of Number Theory, 2018We relate geometric polynomials and [Formula: see text]-Bernoulli polynomials with an integral representation, then obtain several properties of [Formula: see text]-Bernoulli polynomials. These results yield new identities for Bernoulli numbers. Moreover, we evaluate a Faulhaber-type summation in terms of [Formula: see text]-Bernoulli polynomials ...
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Remarks on some relationships between the Bernoulli and Euler polynomials
Applied Mathematics Letters, 2004H M Srivastava, A Pintér
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Some Identities for Euler and Bernoulli Polynomials and Their Zeros
Axioms, 2018Taekyun Kim +2 more
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Some results on the Apostol–Bernoulli and Apostol–Euler polynomials
Computers and Mathematics With Applications, 2008Weiping Wang, Cangzhi Jia
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Some new identities for the Apostol–Bernoulli polynomials and the Apostol–Genocchi polynomials
Applied Mathematics and Computation, 2015Yuan He, Serkan Araci, H M Srivastava
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