FeynCalc manual (development version)

 

FCIteratedIntegral

FCIteratedIntegral[f,x,a,b] is a special head indicating that the function ff represents an iterated integral or a linear combination thereof and that it should be integrated in xx from aa to bb. This notation is understood by the function FCIteratedIntegralEvaluate that does the actual integration.

Notice that before applying FCIteratedIntegralEvaluate all rational functions of xx in ff should be converted to the FCPartialFractionFormrepresentation.

See also

Overview, FCIteratedIntegralEvaluate, ToFCPartialFractionForm

Examples

fun = 1/(1 + x)

1x+1\frac{1}{x+1}

int = FCIteratedIntegral[ToFCPartialFractionForm[fun, x], x, a, b]

FCIteratedIntegral(FCPartialFractionForm(0,({x+1,1}1),x),x,a,b)\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x+1,-1\} & 1 \\ \end{array} \right),x\right),x,a,b\right)

FCIteratedIntegralEvaluate[int]

G(1;b)G(1;a)G(-1; b)-G(-1; a)