AbstractIn this work, the authors present several formulas which compute the following Euler’s type and Dilcher’s type sums of the products of Bernoulli numbers Bn: Ωn(m)≔∑j1+⋯+jm=n(j1,…,jm≧1)2n2j1,…,2jmB2j1⋯B2jm and Δn(m)≔∑j1+⋯+jm=n(j1,…,jm≧0)2n2j1,…,2jmB2j1⋯B2jm respectively, where nk1,…,km=n!k1!⋯km! denotes, as usual, the multinomial coefficient
An investigation of the origin of the formulas for the sums of integer powers was performed. A metho...
AbstractEuler's well-known nonlinear relation for Bernoulli numbers, which can be written in symboli...
In the year 2014, Kim et al. computed a kind of new sums of the products of an arbitrary number of t...
AbstractClosed expressions are obtained for sums of products of Bernoulli numbers of the form[formul...
AbstractClosed expressions are obtained for sums of products of Kronecker's double series of the for...
In this paper, a further investigation for the Apostol-Bernoulli and Apostol-Euler polynomials and n...
We investigate some formulae for the product of two Bernoulli and Euler polynomials arising from the...
AbstractIn this paper, our aim is to investigate the summation form of Bernoulli numbers Bn, such as...
In a recent paper [Montes Taurus J. Pure Appl. Math. 3 (1) (2021), 38–61] we defined the class of c...
AbstractIn this paper we study recurrences concerning the combinatorial sum nrm=∑k≡r(modm)nk and the...
Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials are established by ...
AbstractWe extend Euler's well-known quadratic recurrence relation for Bernoulli numbers, which can ...
We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in ...
Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials are established by ...
AbstractWe give a formula for sums of products of hypergeometric Bernoulli numbers. This formula is ...
An investigation of the origin of the formulas for the sums of integer powers was performed. A metho...
AbstractEuler's well-known nonlinear relation for Bernoulli numbers, which can be written in symboli...
In the year 2014, Kim et al. computed a kind of new sums of the products of an arbitrary number of t...
AbstractClosed expressions are obtained for sums of products of Bernoulli numbers of the form[formul...
AbstractClosed expressions are obtained for sums of products of Kronecker's double series of the for...
In this paper, a further investigation for the Apostol-Bernoulli and Apostol-Euler polynomials and n...
We investigate some formulae for the product of two Bernoulli and Euler polynomials arising from the...
AbstractIn this paper, our aim is to investigate the summation form of Bernoulli numbers Bn, such as...
In a recent paper [Montes Taurus J. Pure Appl. Math. 3 (1) (2021), 38–61] we defined the class of c...
AbstractIn this paper we study recurrences concerning the combinatorial sum nrm=∑k≡r(modm)nk and the...
Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials are established by ...
AbstractWe extend Euler's well-known quadratic recurrence relation for Bernoulli numbers, which can ...
We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in ...
Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials are established by ...
AbstractWe give a formula for sums of products of hypergeometric Bernoulli numbers. This formula is ...
An investigation of the origin of the formulas for the sums of integer powers was performed. A metho...
AbstractEuler's well-known nonlinear relation for Bernoulli numbers, which can be written in symboli...
In the year 2014, Kim et al. computed a kind of new sums of the products of an arbitrary number of t...
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