A function which arises in the fractional integral of e^(a t), given by E_t(ν, a) | = | e^(a t)/(Γ(ν)) integral_0^t x^(ν - 1) e^(-a x) d x | = | (a^(-ν) e^(a t) γ(ν, a t))/(Γ(ν)), where γ(a, z) is the incomplete gamma function and Γ(z) the complete gamma function. The E_t function satisfies the recurrence relation E_t(ν, a) = a E_t(ν + 1, a) + t^ν/(Γ(ν + 1)).

E_n-function | fractional calculus | fractional integral