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EXPANDGA.SM
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1993-10-16
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536b
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13 lines
# expandGa expands gamma(n,x) into x^n*e^-x + ...
# gamma(n,x) is the incomplete gamma function, gamma(n,x)=
# inte(t^n*e^(-t), t,0,x), d(gamma(n,x),x)=x^n*e^(-x).
# gamma(n,0)=0, gamma(n,inf)=gamma(n+1)=n!.
# gamma(n) is the gamma function Γ(n), gamma(n)=inte(t^(n-1)*e^(-t), t,0,inf).
# gamma(n,x) is similar to gamma(n), but its power term is t^n, instead
# of t^(n-1). gamma(n)=(n-1)!.
# See also: gamma, ei, expandEi.
gamma(n_,x_) := if(n>=1, n*gamma(n-1,x)-x^n*e^-x,
if(n<-1, (gamma(n+1,x)-x^(n+1)*e^-x)/(n+1)))