A note on certain inequalities for the gamma function.
A Note on Hölder's Theorem Concerning the Gamma Function.
A note on Mathieu's inequality.
A Note on the Hurwitz Zeta Function
A note on the successive remainders of the exponential series.
A proof of Euler's identity by a functional equation.
A proof of Schur's conjecture and an improvement.
A recovery of Brouncker's proof for the quadrature continued fraction.
350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/π. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis' remarks presented in his Arithmetica Infinitorum. We show that Brouncker's and Wallis' formulas can be extended to MacLaurin's sinusoidal spirals via related Euler's products. We derive Ramanujan's...
A remark on the Lion-Rolin Preparation Theorem for LA-functions
A correct formulation of the Lion-Rolin Preparation Theorem for logarithmic-subanalytic functions (LA-functions) is given.
A restricted Epstein zeta function and the evaluation of some definite integrals
A sharp inequality involving the psi function.
A Short Proof of Selberg's Generalized Beta Formula.
Abschätzung der unvollständigen Beta-Funktion in mehreren reellen Variablen und Parametern.
An asymptotic expansion for a ratio of products of gamma functions.
An explicit evaluation of the Gosper sum.
An identity for sums of polylogarithm functions.
An inequality for the beta function with application to pluripotential theory.
An inequality for the product of two integrals relating to the incomplete gamma function.
An integral involving the generalized zeta function.
An integral transform and its application in the propagation of Lorentz-Gaussian beams
The aim of the present note is to derive an integral transform involving the product of the Whittaker function and the Bessel function of the first kind of order . As a by-product, we also derive certain new integral transforms as particular cases for some special values of the parameters and of the Whittaker function. Eventually, we show the application of the integral in the propagation of hollow higher-order circular Lorentz-cosh-Gaussian beams through an ABCD optical system (see,...