On Hermite expansions of and ln|x|
On Hermite-Hermite matrix polynomials
In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite matrix polynomials is proposed.
On hypergeometric functions and Pochhammer -symbol.
On hypergeometric-type generating relations associated with the generalized zeta function.
On inequalities for hypergeometric analogues of the arithmetic-geometric mean.
On integral forms of generalised Mathieu series.
On integral operator defined by convolution involving hybergeometric functions.
On integral representations of -gamma and -beta functions
We study -integral representations of the -gamma and the -beta functions. As an application of these integral representations, we obtain a simple conceptual proof of a family of identities for Jacobi triple product, including Jacobi's identity, and of Ramanujan's formula for the bilateral hypergeometric series.
On integral transforms.
On interpolation functions of the generalized twisted -Euler polynomials.
On inversion of -transform in -space.
On Kadell's two conjectures for the -Dyson product.
On Kaluza's sign criterion for reciprocal power series
T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.
On Legendre numbers.
On Lindelöf's error bound for Stirling's series.
On linear combinations of two orthogonal polynomial sequences on the unit circle.
On Maslanka's representation for the Riemann zeta function.
On modified asymptotic series involving confluent hypergeometric functions.
On multiple interpolation functions of the Nörlund-type -Euler polynomials.
On multiple twisted -adic -Euler -functions and -functions.