FeynCalc manual (development version)

FCIteratedIntegral

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

Notice that before applying FCIteratedIntegralEvaluate all rational functions of $x$ in $f$ should be converted to the FCPartialFractionFormrepresentation.

See also

Overview, FCIteratedIntegralEvaluate, ToFCPartialFractionForm

Examples

fun = 1/(1 + x)

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

int = FCIteratedIntegral[ToFCPartialFractionForm[fun, 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]

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