FeynCalc manual (development version)

FourSeries

FourSeries[exp, {p,p0,n}] calculates Taylor series of exp w.r.t the 4-vector p to nth order. If the expression diverges at p = p_0, it will be returned unevaluated.

See also

Overview, FourDivergence, ThreeDivergence.

Examples

(m^2 + SPD[p, q]) FAD[{k}, {k + p}] 
 
FourSeries[%, {p, 0, 2}]

\frac{m^2+p\cdot q}{k^2.(k+p)^2}

\frac{4 m^2 (k\cdot p)^2}{\left(k^2\right)^4}-\frac{m^2 p^2}{\left(k^2\right)^3}-\frac{2 m^2 (k\cdot p)}{\left(k^2\right)^3}+\frac{m^2}{\left(k^2\right)^2}+\frac{p\cdot q}{\left(k^2\right)^2}-\frac{2 (k\cdot p) (p\cdot q)}{\left(k^2\right)^3}

```mathematica (SPD[p, q]) DiracTrace[GAD[mu] . GSD[p + q] . GAD[nu]]

FourSeries[%, {p, 0, 2}]

```mathematica

(p\cdot q) \;\text{tr}\left(\gamma ^{\text{mu}}.(\gamma \cdot (p+q)).\gamma ^{\text{nu}}\right)

(p\cdot q) \;\text{tr}\left(\gamma ^{\text{mu}}.(\gamma \cdot p).\gamma ^{\text{nu}}\right)+(p\cdot q) \;\text{tr}\left(\gamma ^{\text{mu}}.(\gamma \cdot q).\gamma ^{\text{nu}}\right)