PaXDiscExpand
PaXDiscExpand
is an option for PaXEvaluate
.
If set to True
, Package-X function DiscExpand
will be applied to the output of Package-X thus replacing
DiscB
by its explicit form.
See also
Overview , PaXEvaluate .
Examples
PaVe[ 0 , 0 , 1 , { SP[ p , p ], 0 , m ^ 2 }, { m ^ 2 , m ^ 2 , m ^ 2 }]
PaXEvaluate[ % ]
C 001 ( 0 , p ‾ 2 , m 2 , m 2 , m 2 , m 2 ) \text{C}_{001}\left(0,\overline{p}^2,m^2,m^2,m^2,m^2\right) C 001 ( 0 , p 2 , m 2 , m 2 , m 2 , m 2 )
− 35 m 2 36 ( m 2 − p ‾ 2 ) + 2 p ‾ 2 9 ( m 2 − p ‾ 2 ) + m 2 p ‾ 2 ( p ‾ 2 − 4 m 2 ) log ( p ‾ 2 ( p ‾ 2 − 4 m 2 ) − p ‾ 2 + 2 m 2 2 m 2 ) 2 ( m 2 − p ‾ 2 ) 2 − p ‾ 2 p ‾ 2 ( p ‾ 2 − 4 m 2 ) log ( p ‾ 2 ( p ‾ 2 − 4 m 2 ) − p ‾ 2 + 2 m 2 2 m 2 ) 12 ( m 2 − p ‾ 2 ) 2 + π ( 9 3 + π ) m 4 36 ( m 2 − p ‾ 2 ) 2 + m 4 log 2 ( p ‾ 2 ( p ‾ 2 − 4 m 2 ) − p ‾ 2 + 2 m 2 2 m 2 ) 4 ( m 2 − p ‾ 2 ) 2 + m 4 p ‾ 2 ( p ‾ 2 − 4 m 2 ) log ( p ‾ 2 ( p ‾ 2 − 4 m 2 ) − p ‾ 2 + 2 m 2 2 m 2 ) 3 p ‾ 2 ( m 2 − p ‾ 2 ) 2 − 1 12 ε + 1 12 ( − log ( μ 2 m 2 ) + γ − log ( 4 π ) + 2 log ( 2 π ) ) -\frac{35 m^2}{36
\left(m^2-\overline{p}^2\right)}+\frac{2 \overline{p}^2}{9
\left(m^2-\overline{p}^2\right)}+\frac{m^2 \sqrt{\overline{p}^2
\left(\overline{p}^2-4 m^2\right)} \log \left(\frac{\sqrt{\overline{p}^2
\left(\overline{p}^2-4 m^2\right)}-\overline{p}^2+2 m^2}{2
m^2}\right)}{2 \left(m^2-\overline{p}^2\right)^2}-\frac{\overline{p}^2
\sqrt{\overline{p}^2 \left(\overline{p}^2-4 m^2\right)} \log
\left(\frac{\sqrt{\overline{p}^2 \left(\overline{p}^2-4
m^2\right)}-\overline{p}^2+2 m^2}{2 m^2}\right)}{12
\left(m^2-\overline{p}^2\right)^2}+\frac{\pi \left(9 \sqrt{3}+\pi
\right) m^4}{36 \left(m^2-\overline{p}^2\right)^2}+\frac{m^4 \log
^2\left(\frac{\sqrt{\overline{p}^2 \left(\overline{p}^2-4
m^2\right)}-\overline{p}^2+2 m^2}{2 m^2}\right)}{4
\left(m^2-\overline{p}^2\right)^2}+\frac{m^4 \sqrt{\overline{p}^2
\left(\overline{p}^2-4 m^2\right)} \log \left(\frac{\sqrt{\overline{p}^2
\left(\overline{p}^2-4 m^2\right)}-\overline{p}^2+2 m^2}{2
m^2}\right)}{3 \overline{p}^2
\left(m^2-\overline{p}^2\right)^2}-\frac{1}{12 \varepsilon
}+\frac{1}{12} \left(-\log \left(\frac{\mu ^2}{m^2}\right)+\gamma -\log
(4 \pi )+2 \log (2 \pi )\right) − 36 ( m 2 − p 2 ) 35 m 2 + 9 ( m 2 − p 2 ) 2 p 2 + 2 ( m 2 − p 2 ) 2 m 2 p 2 ( p 2 − 4 m 2 ) log ( 2 m 2 p 2 ( p 2 − 4 m 2 ) − p 2 + 2 m 2 ) − 12 ( m 2 − p 2 ) 2 p 2 p 2 ( p 2 − 4 m 2 ) log ( 2 m 2 p 2 ( p 2 − 4 m 2 ) − p 2 + 2 m 2 ) + 36 ( m 2 − p 2 ) 2 π ( 9 3 + π ) m 4 + 4 ( m 2 − p 2 ) 2 m 4 log 2 ( 2 m 2 p 2 ( p 2 − 4 m 2 ) − p 2 + 2 m 2 ) + 3 p 2 ( m 2 − p 2 ) 2 m 4 p 2 ( p 2 − 4 m 2 ) log ( 2 m 2 p 2 ( p 2 − 4 m 2 ) − p 2 + 2 m 2 ) − 12 ε 1 + 12 1 ( − log ( m 2 μ 2 ) + γ − log ( 4 π ) + 2 log ( 2 π ) )
PaVe[ 0 , 0 , 1 , { SP[ p , p ], 0 , m ^ 2 }, { m ^ 2 , m ^ 2 , m ^ 2 }]
PaXEvaluate[ % , PaXDiscExpand -> False ]
C 001 ( 0 , p ‾ 2 , m 2 , m 2 , m 2 , m 2 ) \text{C}_{001}\left(0,\overline{p}^2,m^2,m^2,m^2,m^2\right) C 001 ( 0 , p 2 , m 2 , m 2 , m 2 , m 2 )
m 2 p ‾ 2 ( Λ ( p ‾ 2 , m , m ) ) 2 ( m 2 − p ‾ 2 ) 2 − p ‾ 4 ( Λ ( p ‾ 2 , m , m ) ) 12 ( m 2 − p ‾ 2 ) 2 + m 4 ( Λ ( p ‾ 2 , m , m ) ) 3 ( m 2 − p ‾ 2 ) 2 − m 2 p ‾ 2 ( − 6 log ( μ 2 m 2 ) + 6 γ − 43 + 6 log ( π ) ) 36 ( m 2 − p ‾ 2 ) 2 + p ‾ 4 ( − 3 log ( μ 2 m 2 ) + 3 γ − 8 + 3 log ( π ) ) 36 ( m 2 − p ‾ 2 ) 2 + m 4 ( − 3 log ( μ 2 m 2 ) + π 2 + 9 3 π + 3 γ − 35 − 3 log ( 4 π ) + 6 log ( 2 π ) ) 36 ( m 2 − p ‾ 2 ) 2 + m 4 log 2 ( p ‾ 2 ( p ‾ 2 − 4 m 2 ) − p ‾ 2 + 2 m 2 2 m 2 ) 4 ( m 2 − p ‾ 2 ) 2 − 1 12 ε \frac{m^2 \overline{p}^2 \left(\Lambda
(\overline{p}^2,m,m)\right)}{2
\left(m^2-\overline{p}^2\right)^2}-\frac{\overline{p}^4 \left(\Lambda
(\overline{p}^2,m,m)\right)}{12
\left(m^2-\overline{p}^2\right)^2}+\frac{m^4 \left(\Lambda
(\overline{p}^2,m,m)\right)}{3
\left(m^2-\overline{p}^2\right)^2}-\frac{m^2 \overline{p}^2 \left(-6
\log \left(\frac{\mu ^2}{m^2}\right)+6 \gamma -43+6 \log (\pi
)\right)}{36 \left(m^2-\overline{p}^2\right)^2}+\frac{\overline{p}^4
\left(-3 \log \left(\frac{\mu ^2}{m^2}\right)+3 \gamma -8+3 \log (\pi
)\right)}{36 \left(m^2-\overline{p}^2\right)^2}+\frac{m^4 \left(-3 \log
\left(\frac{\mu ^2}{m^2}\right)+\pi ^2+9 \sqrt{3} \pi +3 \gamma -35-3
\log (4 \pi )+6 \log (2 \pi )\right)}{36
\left(m^2-\overline{p}^2\right)^2}+\frac{m^4 \log
^2\left(\frac{\sqrt{\overline{p}^2 \left(\overline{p}^2-4
m^2\right)}-\overline{p}^2+2 m^2}{2 m^2}\right)}{4
\left(m^2-\overline{p}^2\right)^2}-\frac{1}{12 \varepsilon } 2 ( m 2 − p 2 ) 2 m 2 p 2 ( Λ ( p 2 , m , m ) ) − 12 ( m 2 − p 2 ) 2 p 4 ( Λ ( p 2 , m , m ) ) + 3 ( m 2 − p 2 ) 2 m 4 ( Λ ( p 2 , m , m ) ) − 36 ( m 2 − p 2 ) 2 m 2 p 2 ( − 6 log ( m 2 μ 2 ) + 6 γ − 43 + 6 log ( π ) ) + 36 ( m 2 − p 2 ) 2 p 4 ( − 3 log ( m 2 μ 2 ) + 3 γ − 8 + 3 log ( π ) ) + 36 ( m 2 − p 2 ) 2 m 4 ( − 3 log ( m 2 μ 2 ) + π 2 + 9 3 π + 3 γ − 35 − 3 log ( 4 π ) + 6 log ( 2 π ) ) + 4 ( m 2 − p 2 ) 2 m 4 log 2 ( 2 m 2 p 2 ( p 2 − 4 m 2 ) − p 2 + 2 m 2 ) − 12 ε 1