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]

$$g(x) \delta (1-x)$$

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

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

$$g(x) \delta '(1-x)$$

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

$$x \log (x) \delta '(1-x)$$

$$\delta (1-x)$$

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

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

$$-\delta (1-x)$$

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

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

$$0$$

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

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

$$-\delta (1-x)$$