A short note on higher Mordell integrals

A Note on Complete Integrals

We present a theorem concerning the representation of solutions of a first-order partial differential equation in terms of a complete integral of the equation. We discuss the geometrical significance of that theorem.

A Note on Twistor Integrals

This paper is a brief introduction to twistor integrals from a mathematical point of view. It was inspired by a paper of Hodges [H] which we studied in a seminar at Cal Tech directed by Matilde Marcoli. The idea is to write the amplitude for a graph with n loops and 2n + 2 propagators using the geometry of pfaffians for sums of rank 2 alternating matrices. (Hodges considers the case of 1 loop a...

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...

A Note on a Conjecture of L . J . Mordell

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.