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CD ROM Paradise Collection 4
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CD ROM Paradise Collection 4 1995 Nov.iso
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sm32a.zip
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LIBRARY
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EI.LI
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1993-11-14
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838b
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31 lines
# library ei.(x)
# ei(x) is the exponential integral function Ei(x),
# ei(x) = inte(e^t/t, t,-inf,x), d(ei(x),x)=e^x/x,
# ei(n,x) is the exponential integral function En(x),
# ei(n,x)=inte(t^n*e^t, t,-inf,x), d(ei(n,x),x)=x^n*e^x, ei(-1, x)=ei(x),
# ei(0,x)=e^x.
# See also: gamma.sm.
# d(ei(n_,x_),x_):= x^n*e^x
# d(ei(x_) ,x_) := e^x/x
# ei(n_,x_) := if(n>=1, -n*ei(n-1,x)+x^n*e^x,
if(n<-1, (-ei(n+1,x)+x^(n+1)*e^x)/(n+1)))
ei(0) := 1
ei(-inf) := 0
#ei(1):=1
#ei(2):=1
#ei(n_):=if(n>2, if(isinteger(n), (n-1)!, (n-1)*ei(n-1)))
#ei(n_):=if(n>0 and numerical==on, sqrt(2*pi)*n^(n-0.5)*exp(-n)*(1+1/(12*n)))
ei(0,0) := 1
#ei(n_,0) := (-1)^n*n!
#ei(n_,inf) := inf
ei(n_,-inf) := 0
ei(-1,x_) := ei(x)
ei(0,x_) := e^x
ei(-0.5,x_) := -i*sqrt(pi)*erf(i*sqrt(x))
#ei(-1/2,x_) := -i*sqrt(pi)*erf(i*sqrt(x))