Discovering hook length formulas by an expansion technique.
Distribution of crossings, nestings and alignments of two edges in matchings and partitions.
Elementary -identities. (Elementare -Identitäten.)
Explicit plethystic formulas for Macdonald -Kostka coefficients.
Exploring the -Riemann zeta function and -Bernoulli polynomials.
Faber polynomial coefficient estimates of bi-univalent functions connected with the -convolution
We introduce a new class of bi-univalent functions defined in the open unit disc and connected with a -convolution. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class by using Faber polynomial expansions and we obtain an estimation for the Fekete-Szegö problem for this class.
Factors of alternating sums of products of binomial and q-binomial coefficients
Finite Rogers-Ramanujan type identities.
Finite vector spaces and certain lattices.
From double Hecke algebra to analysis.
Generalization of two identities in Ramanujan's lost notebook
Generalized number derivatives.
HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Integer sequences and matrices over finite fields.
Interpolation of entire functions on regular sparse sets and -Taylor series
We give a pure complex variable proof of a theorem by Ismail and Stanton and apply this result in the field of integer-valued entire functions. Our proof rests on a very general interpolation result for entire functions.
Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.
Lagrange inversion.
Mean Value Theorems in q-calculus
Mixed sums of squares and triangular numbers
Multiple twisted -Euler numbers and polynomials associated with -adic -integrals.