Confluent hypergeometric solutions for conduction equation.

Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator

Resat Yilmazer 1, Mustafa Inc 1,*, Fairouz Tchier 2 and Dumitru Baleanu 3,4 1 Department of Mathematics, Science Faculty, Fırat University, Elazığ 23119, Turkey; [email protected] 2 Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia; [email protected] 3 Department of Mathematics and Computer Science, Çankaya University, Ankara 06530, Turkey; dumitru...

Integral relations for solutions of the confluent Heun equation

Abstract: Firstly, we construct kernels for integral relations among solutions of the confluent Heun equation (CHE). Additional kernels are systematically generated by applying substitutions of variables. Secondly, we establish integral relations between known solutions of the CHE that are power series and solutions that are series of special functions. Thirdly, by using one of the integral rel...

Gauss Quadrature Approximations to Hypergeometric and Confluent Hypergeometric Functions

Asymptotic Representations of Confluent Hypergeometric Functions.

I A more general theory will result if in the place of R we employ an abstract normed ring. s We use the symbols =, ... ... in more than one sense. No confusion need arise as tie context makes clear the meaning of each such symbol. It is worth while to mention here that the relation of equality = for E1 as well as for E2 is not an independent primitive idea; for, an equivalent set of postulates...

A Connection Formula for the q-Confluent Hypergeometric Function

We show a connection formula for the q-confluent hypergeometric functions 2φ1(a, b; 0; q, x). Combining our connection formula with Zhang’s connection formula for 2φ0(a, b;−; q, x), we obtain the connection formula for the q-confluent hypergeometric equation in the matrix form. Also we obtain the connection formula of Kummer’s confluent hypergeometric functions by taking the limit q → 1− of our...