Notes on algebraic functions.
Notes on double inequalities of Mathieu's series.
Notiz über die Dirichlet'schen Integralausdrücke für die Kugelfunction. Pn (cos ....) und über eine analoge Integralform für die Cylinderfunction J (x)
Notiz über die Herleitung der hypergeometrischen Differentialgleichung.
Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants
MSC 2010: 11B83, 05A19, 33C45This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the generalized Somos-4 property. Here, we recognize well known number sequences such as: the Fibonacci, Catalan, Motzkin and SchrÄoder sequences, like special cases.
Numerical aspects of the identification of thermal characteristics using the hot-wire method
The hot-wire method, based on the recording of the temperature development in time in a testing sample, supplied by a probe with its own thermal source, is useful to evaluate the thermal conductivity of materials under extremal loads, in particular in refractory brickworks. The formulae in the technical standards come from the analytical solution of the non-stationary equation of heat conduction in cylindric (finally only polar) coordinates for a simplified formulation of boundary conditions, neglecting...
Numerical Calculation of Incomplete Gamma Functions by the Trapezoidal Rule.
Numerical Integration over a Semi-Infinite Interval, Using the Lognormal Distribution.
Numerical Results for the Generalized Mittag-Leffler Function
Mathematics Subject Classification: 33E12, 33FXX PACS (Physics Abstracts Classification Scheme): 02.30.Gp, 02.60.GfResults of extensive calculations for the generalized Mittag-Leffler function E0.8,0.9(z) are presented in the region −8 ≤ Re z ≤ 5 and −10 ≤ Im z ≤ 10 of the complex plane. This function is related to the eigenfunction of a fractional derivative of order α = 0.8 and type β = 0.5.
Numeric-analytical construction of Mathieu functions
In this paper we present an iterative algorithm for the construction of Mathieu functions of any order in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.