A generalized integration formula for indefinite integrals of special functions

A Numerical Integration Method by Using Generalized Series of Functions

Numerical indefinite integration of functions with singularities

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for Hp functions, for p > 1, over the interval (−1, 1). The main factor in the error of our indefinite quadrature formula is O(e−π √ ), with 2N nodes and 1 p + 1 q = 1. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of √ 2 in the constant of the exponential. We conjectur...

a numerical integration method by using generalized series of functions

A Note on Indefinite Integrals

1. G. H. Hardy and M. Riesz, The general theory of Dirichlet's series, London, 1915. 2. E. Kogbetliantz, Sur la sommation des séries divergentes par les moyennes simples et doubles, Ann. École Norm. (3) vol. 42 (1925) pp. 193-216. 3. Otto Szász, Verallgemeinerung eines Littlewood'sehen Salzes über Potenzreihen, J. London Math. Soc. vol. 3 (1928) pp. 254-262. 4. A. Zygmund, Remarque sur la somma...

First Integrals of a Special System of Odes (TECHNICAL NOTE)

In this paper we suggest a method to calculate the first integrals of a special system of the first order of differential equations. Then we use the method for finding the solutions of some differential equations such as, the differential equation of RLC circuit.