General Integral Transform of the Exponential Integrals

Astronomy and Astrophysics – Astrophysics

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Scientific paper

General integral transform of the exponential integralsE n is considered and will be denoted asB {/(k) n }(τ). Different expressions and the equations satisfied byB {/(k) n } are developed. Two-term recurrence formula forB {/(k) n }(0) and three-term recurrence formula forB {/(k) n }(τ); τ≠0 will be established for a givenk≥1 andn=2,3, ...,N. The computational algorithms based on these formulae are also constructed for the casesk=1,2,3, andn≥2. Finally the numerical results fork=2,3 andn=2(1)25 are presented to 15-digit accuracy

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