A functional inequality for the survival function of the gamma distribution.
An inequality for the product of two integrals relating to the incomplete gamma function.
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...
Derangements and applications.
Die multivariate inkomplette Beta-Funktion.
Evaluation of the Fermi-Dirac integral of half-integer order
Further Generalization of Kobayashi's Gamma Function
In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)
Grünbaum-type inequalities for special functions.
Monotonicity properties of the relative error of a Padé approximation for Mills' ratio.
On a form of bi-variate-t distribution.
On Peter's Formula for Probable Error.
Optimization of Rational Approximations by Continued Fractions
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.To get guaranteed machine enclosures of a special function f(x), an upper bound ε(f) of the relative error is needed, where ε(f) itself depends on the error bounds ε(app); ε(eval) of the approximation and evaluation error respectively. The approximation function g(x) ≈ f(x) is a rational function (Remez algorithm), and with sufficiently high polynomial degrees ε(app) becomes...
Schrödinger Equation and Oscillatory Hilbert Transforms of Second Degree.
Some conjectures on the zeros of approximates to the Riemann ≡-function and incomplete gamma functions
Riemann conjectured that all the zeros of the Riemann ≡-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums ≡N(z) in Riemann’s uniformly convergent infinite series expansion of ≡(z) involving incomplete gamma functions. We conjecture that when the zeros of ≡N(z) in the first quadrant of the complex plane are listed by increasing real part, their imaginary parts are monotone nondecreasing. We show how this...
Some inequalities of the incomplete gamma and related functions.
Some properties of the incomplete beta function ratio
Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions.
Three Digit Accurate Multiple Normal Probabilities.
Über ein Problem der Näherungsrechnung und die Makeham'schen Rentenwerte
Обращение одного интегрального оператора методом разложения по ортогональным операторам Ватсона