Double-exponential formula for infinite integrals of unilateral rapidly decreasing functions

Abstract

Double-exponential formulas were proposed by Takahasi and Mori in 1974 as efficient numerical integration methods. They considered four typical cases: (i) integral on a finite interval, (ii) semi-infinite integral of algebraically decaying functions, (iii) semi-infinite integral of exponentially decaying functions, (iv) infinite integral of algebraically decaying functions, and they proposed a double-exponential formula for each case. This paper proposes a double-exponential formula for another case: (v) infinite integral of unilateral rapidly decreasing functions. A theoretical error analysis of the proposed formula is also given.