## Et-Function

A function which arises in Fractional Calculus.

 (1)

where is the incomplete Gamma Function and the complete Gamma Function. The function satisfies the Recurrence Relation
 (2)

A special value is
 (3)

Abramowitz, M. and Stegun, C. A. (Eds.). Exponential Integral and Related Functions.'' Ch. 5 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 227-233, 1972.