Identitäten bei den Stirling-Zahlen 2.Art aus kombinatorischen Überlegungen beim Würfelspiel.
Identities arising from higher-order Daehee polynomial bases
Here we will derive formulas for expressing any polynomial as linear combinations of two kinds of higherorder Daehee polynomial basis. Then we will apply these formulas to certain polynomials in order to get new and interesting identities involving higher-order Daehee polynomials of the first kind and of the second kind.
Identities concerning Bernoulli and Euler polynomials
Identities derived from noncrossing partitions of type .
Identities involving reciprocals of binomial coefficients.
Improved inclusion-exclusion identities and inequalities based on a particular class of abstract tubes.
Infinite products over hyperpyramid lattices.
Infinite products over visible lattice points.
Integral representation of the -th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel
In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges–Rovnyak spaces , where is in the unit ball of . In particular, we generalize a result of Ahern–Clark obtained for functions of the model spaces , where is an inner function. Using hypergeometric series, we obtain a nontrivial formula of combinatorics for sums of binomial coefficients. Then we apply this formula to show the norm convergence of reproducing kernel of evaluation...
Integrals and polygamma representations for binomial sums.
Integrals of logarithmic and hypergeometric functions
Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler sums. In this paper we explore many relations and explicitly derive closed form representations of integrals of logarithmic, hypergeometric functions and the Lerch phi transcendent in terms of zeta functions and sums of alternating harmonic numbers.
Integration over a Simplex, Truncated Cubes, and Eulerian Numbers.
Introduction aux polyèdres en combinatoire d'après E. Ehrhart et R. Stanley
Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.
Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.
A pair of simple bivariate inverse series relations are used by embedding machinery to produce several double summation formulae on shifted factorials (or binomial coefficients), including the evaluation due to Blodgett-Gessel. Their q-analogues are established in the second section. Some generalized convolutions are presented through formal power series manipulation.
Inversion techniques and combinatorial identities. A unified treatment for the 7f6-series identities.
Inversion techniques and combinatorial identities. Jackson’s -analogue of the Dougall-Dixon theorem and the dual formulae
Inversion techniques and combinatorial identities. Strange evaluations of basic hypergeometric series
Irreduzible Polynome als kombinatorische Figuren.