FeynCalc manual (development version)

SimplifyDeltaFunction

SimplifyDeltaFunction[exp, x] simplifies f[x]*DeltaFunction[1-x] to Limit[f[x],x->1] DeltaFunction[1-x] and applies a list of transformation rules for DeltaFunctionPrime[1-x]*x^(OPEm-1)*f[x] where x^(OPEm-1) is suppressed in exp.

See also

Overview, DeltaFunction, DeltaFunctionPrime.

Examples

g[x] DeltaFunction[1 - x] 
 
SimplifyDeltaFunction[ %, x]

g(x)δ(1x)g(x) \delta (1-x)

δ(1x)limx1g(x)\delta (1-x) \underset{x\to 1}{\text{lim}}g(x)

g[x] DeltaFunctionPrime[1 - x] 
 
SimplifyDeltaFunction[ %, x] 
 
x Log[x] DeltaFunctionPrime[1 - x] 
 
SimplifyDeltaFunction[ %, x]

g(x)δ(1x)g(x) \delta '(1-x)

δ(1x)limx1g(x)+δ(1x)limx1g(x)\delta (1-x) \underset{x\to 1}{\text{lim}}g'(x)+\delta '(1-x) \underset{x\to 1}{\text{lim}}g(x)

xlog(x)δ(1x)x \log (x) \delta '(1-x)

δ(1x)\delta (1-x)

PolyLog[2, 1 - x] DeltaFunctionPrime[1 - x] 
 
SimplifyDeltaFunction[ %, x]

Li2(1x)δ(1x)\text{Li}_2(1-x) \delta '(1-x)

δ(1x)-\delta (1-x)

Log[x] PolyLog[2, 1 - x] DeltaFunctionPrime[1 - x] 
 
SimplifyDeltaFunction[ %, x]

Li2(1x)log(x)δ(1x)\text{Li}_2(1-x) \log (x) \delta '(1-x)

00

PolyLog[3, 1 - x] DeltaFunctionPrime[1 - x] 
 
SimplifyDeltaFunction[ %, x]

Li3(1x)δ(1x)\text{Li}_3(1-x) \delta '(1-x)

δ(1x)-\delta (1-x)