FeynCalc manual (development version)

 

ToFCPartialFractionForm

ToFCPartialFractionForm[exp, x] converts sums of rational functions of the form n+f1[xr1]1p+f2[xr2]2p+n + \frac{f_1}{[x-r_1]^p_1} + \frac{f_2}{[x-r_2]^p_2} + \ldots to FCPartialFractionForm[n, {{f1,x-r1,p1},{f2,x-r2,p2}, ...}, x].

This facilitates the handling of iterated integrals.

See also

Overview, FCPartialFractionForm, FromFCPartialFractionForm.

Examples

x/(x + 1) 
 
ToFCPartialFractionForm[%, x]

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

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

1/(x^2 + 3) 
 
ToFCPartialFractionForm[%, x]

1x2+3\frac{1}{x^2+3}

FCPartialFractionForm(0,({xi3,1}i23{x+i3,1}i23),x)\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \left\{x-i \sqrt{3},-1\right\} & -\frac{i}{2 \sqrt{3}} \\ \left\{x+i \sqrt{3},-1\right\} & \frac{i}{2 \sqrt{3}} \\ \end{array} \right),x\right)

(-64*(-1 + z^2))/(15*(1 + z^2 + z^4)) 
 
ToFCPartialFractionForm[%, z]

64(z21)15(z4+z2+1)-\frac{64 \left(z^2-1\right)}{15 \left(z^4+z^2+1\right)}

FCPartialFractionForm(0,({z13,1}3215{z+13,1}3215{z(1)2/3,1}3215{z+(1)2/3,1}3215),z)\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \left\{z-\sqrt[3]{-1},-1\right\} & -\frac{32}{15} \\ \left\{z+\sqrt[3]{-1},-1\right\} & \frac{32}{15} \\ \left\{z-(-1)^{2/3},-1\right\} & \frac{32}{15} \\ \left\{z+(-1)^{2/3},-1\right\} & -\frac{32}{15} \\ \end{array} \right),z\right)