FeynCalc manual (development version)

 

FCIteratedIntegralSimplify

FCIteratedIntegralSimplify[ex] uses linearity to simplify nested products and linear combinations of FCIteratedIntegrals.

See also

Overview, FCIteratedIntegral, FCIteratedIntegral, FCGPL.

Examples

int = C[1, 0] + Epsilon*(C[1, 1] + FCIteratedIntegral[C[1, 0]*FCPartialFractionForm[0, {{{x, -1}, -2}}, x], x]) + 
   Epsilon^2*(C[1, 2] + FCIteratedIntegral[(C[1, 1] + FCIteratedIntegral[C[1, 0]*FCPartialFractionForm[0, 
             {{{x, -1}, -2}}, x], x])*FCPartialFractionForm[0, {{{x, -1}, -2}}, x], x]) + 
   Epsilon^3*(C[1, 3] + FCIteratedIntegral[(C[1, 2] + FCIteratedIntegral[(C[1, 1] + 
              FCIteratedIntegral[C[1, 0]*FCPartialFractionForm[0, {{{x, -1}, -2}}, x], x])*FCPartialFractionForm[0, 
             {{{x, -1}, -2}}, x], x])*FCPartialFractionForm[0, {{{x, -1}, -2}}, x], x])

ε3(FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x)(FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x)(FCIteratedIntegral(C[1,0]  FCPartialFractionForm(0,({x,1}2),x),x)+C[1,1]),x)+C[1,2]),x)+C[1,3])+ε2(FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x)(FCIteratedIntegral(C[1,0]  FCPartialFractionForm(0,({x,1}2),x),x)+C[1,1]),x)+C[1,2])+ε(FCIteratedIntegral(C[1,0]  FCPartialFractionForm(0,({x,1}2),x),x)+C[1,1])+C[1,0]\varepsilon ^3 \left(\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right) \left(\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right) \left(\text{FCIteratedIntegral}\left(C[1,0] \;\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x\right)+C[1,1]\right),x\right)+C[1,2]\right),x\right)+C[1,3]\right)+\varepsilon ^2 \left(\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right) \left(\text{FCIteratedIntegral}\left(C[1,0] \;\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x\right)+C[1,1]\right),x\right)+C[1,2]\right)+\varepsilon \left(\text{FCIteratedIntegral}\left(C[1,0] \;\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x\right)+C[1,1]\right)+C[1,0]

FCIteratedIntegralSimplify[int]

ε3(C[1,2]  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x),x)+C[1,1]  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x)  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x),x),x)+C[1,0]  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x)  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x)  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x),x),x),x)+C[1,3])+ε2(C[1,1]  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x),x)+C[1,0]  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x)  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x),x),x)+C[1,2])+ε(C[1,0]  FCIteratedIntegral(FCPartialFractionForm(0,({x,1}2),x),x)+C[1,1])+C[1,0]\varepsilon ^3 \left(C[1,2] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x\right)+C[1,1] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right) \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x\right),x\right)+C[1,0] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right) \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right) \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x\right),x\right),x\right)+C[1,3]\right)+\varepsilon ^2 \left(C[1,1] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x\right)+C[1,0] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right) \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x\right),x\right)+C[1,2]\right)+\varepsilon \left(C[1,0] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x\right)+C[1,1]\right)+C[1,0]