Series Solution of the Pantograph Equation and Its Properties

[摘要] In this paper, we discuss the classical pantograph equation and its generalizations to include fractional order and the higher order case. The special functions are obtained from the series solution of these equations. We study different properties of these special functions and establish the relation with other functions. Further, we discuss some contiguous relations for these special functions.

[学科分类] 数值分析

[关键词] pantograph equation;proportional delay;fractional derivative;Gaussian binomial coefficient