Exponential sums and certain hypergeometric type initial value problems

Abstract

A technique involving exponential functions is given for constructing solutions or approximate solutions of hypergeometric problems of the form

in which The method makes use of undetermined coefficients for solving an infinite system of coupled differential equations and leads to simple criteria for deciding when the solution must contain logarithmic terms. An elementary algorithm for solving linear non-homogeneous two term recurrence relations is provided.

Keywords:

• Hypergeometric type problem
• exceptional problem
• logarithmic terms
• recurrence relations
• exponential terms
• system of matrix equations

AMS(MOS)::

• 34A25
• 33A35
• 35Q05