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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | )abbrev category LFCAT LiouvillianFunctionCategory
++ Category for the transcendental Liouvillian functions
++ Author: Manuel Bronstein
++ Date Last Updated: 14 May 1991
++ Description:
++ Category for the transcendental Liouvillian functions;
LiouvillianFunctionCategory() : Category == SIG where
SIG ==> Join(PrimitiveFunctionCategory, TranscendentalFunctionCategory) with
Ei : $ -> $
++ Ei(x) returns the exponential integral of x, that is,
++ the integral of \spad{exp(x)/x dx}.
Si : $ -> $
++ Si(x) returns the sine integral of x, that is,
++ the integral of \spad{sin(x) / x dx}.
Ci : $ -> $
++ Ci(x) returns the cosine integral of x, that is,
++ the integral of \spad{cos(x) / x dx}.
li : $ -> $
++ li(x) returns the logarithmic integral of x, that is,
++ the integral of \spad{dx / log(x)}.
dilog : $ -> $
++ dilog(x) returns the dilogarithm of x, that is,
++ the integral of \spad{log(x) / (1 - x) dx}.
erf : $ -> $
++ erf(x) returns the error function of x, that is,
++ \spad{2 / sqrt(%pi)} times the integral of \spad{exp(-x**2) dx}.
fresnelS : $ -> $
++ fresnelS(x) is the Fresnel integral S, defined by
++ S(x) = integrate(sin(t^2),t=0..x)
fresnelC : $ -> $
++ fresnelC(x) is the Fresnel integral C, defined by
++ C(x) = integrate(cos(t^2),t=0..x)
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