Discrete complementary exponential and sine integral functions

Abstract

Discrete analogues of the sine integral and complementary exponential integral functions are investigated. Hypergeometric representation, power series, and Laplace transforms are derived for each. The difficulties in extending these definitions to other common trigonometric integral functions are discussed.

Keywords

• discrete special function
• generalized hypergeometric
• sine integral
• exponential integral
• difference equation
• primary: 33c20
• secondary: 33c47
• 44a20
• 39a06