A computer proof of Turán's inequality.
A proof of a conjecture of Knuth.
About a new kind of Ramanujan-type series.
Accelerated series for universal constants, by the WZ method.
Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values
2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function. Even if the focus is mainly on the real arguments’ values, the methods introduced here can be used in the complex plane, too. The approaches presented in the paper include integral representations of the Wright function, its asymptotic expansions and summation of series. Because the Wright function depends on two parameters ...
An accurate approximation of zeta-generalized-Euler-constant functions
Zeta-generalized-Euler-constant functions, and defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and (1) = ln , are studied and estimated with high accuracy.
An Apéry-like difference equation for Catalan's constant.
Analytic and combinatoric aspects of Hurwitz polyzêtas
In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to build the...
Apéry's double sum is plain sailing indeed.
Application of Bessel coefficients in approximative expressing of collectives
Approximating poles of complex rational functions.
Approximating real Pochhammer products: a comparison with powers
Accurate estimates of real Pochhammer products, lower (falling) and upper (rising), are presented. Double inequalities comparing the Pochhammer products with powers are given. Several examples showing how to use the established approximations are stated.
Approximation of hypergeometric functions with matricial argument through their development in series of zonal polynomials.