FCIteratedIntegralEvaluate
FCIteratedIntegralEvaluate[ex]
evaluates iterated integrals in ex in terms of multiple polylogarithms.
To that aim the ex
must contain ration functions (in the FCPartialFractionForm
notation) and possibly FCGPL
s wrapped with FCIteratedIntegral
heads
See also
Overview, FCIteratedIntegral, FCIteratedIntegralSimplify, FCGPL.
Examples
int = FCPartialFractionForm[0, {{{-a + x[2], -1}, (1 + a + x[3])^(-2)},
{{1 + x[2] + x[3], -2}, -(1 + a + x[3])^(-1)}, {{1 + x[2] + x[3], -1}, -(1 + a + x[3])^(-2)}}, x[2]]
FCPartialFractionForm0,{x(2)−a,−1}{x(2)+x(3)+1,−2}{x(2)+x(3)+1,−1}(a+x(3)+1)21−a+x(3)+11−(a+x(3)+1)21,x(2)
FCIteratedIntegralEvaluate[FCIteratedIntegral[int, x[2], 0, Infinity]]
−FCPartialFractionForm(0,({∞,−1}−a+x(3)+11),∞)+FCPartialFractionForm(0,({x(3)+1,−1}−a+x(3)+11),0)−(a+x(3)+1)2G(−x[3]−1;∞)+(a+x(3)+1)2G(a;∞)
FCIteratedIntegralEvaluate[FCIteratedIntegral[int, x[2], 0, x[2]]]
FCPartialFractionForm(0,({x(3)+1,−1}−a+x(3)+11),0)−FCPartialFractionForm(0,({x(2)+x(3)+1,−1}−a+x(3)+11),x(2))+(a+x(3)+1)2G(a;x[2])−(a+x(3)+1)2G(−x[3]−1;x[2])