One Special Identity between the complete elliptic integrals of the first and the third kind
| dc.creator | Jia, Yu | |
| dc.date | 2008-02-27 | |
| dc.date.accessioned | 2026-07-07T09:23:33Z | |
| dc.date.available | 2026-07-07T09:23:33Z | |
| dc.description | I prove an identity between the first kind and the third kind complete elliptic integrals with the following form: $$Π({(1+x) (1-3 x)\over (1-x) (1+3 x)}, {(1+x)^3(1-3 x)\over (1-x)^3 (1+3x)})- {1+ 3 x \over 6 x} K ({(1+x)^3(1-3x)\over (1-x)^3 (1+3x)}) = 0, (0< x < 1); =-{π\over 12} {(x-1)^{3/2}\sqrt{1+3 x}\over x} (x<0 or x>1).$$ This relation can be applied to eliminate the complete elliptic integral of the third kind from the analytic solutions of the imaginary part of two-loop sunset diagrams in the equal mass case. The validity of this relation in the complex domain is also briefly discussed. | |
| dc.description | 8 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0802.3977 | |
| dc.identifier | http://arxiv.org/abs/0802.3977 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155774 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Phenomenology | |
| dc.subject | General Mathematics | |
| dc.title | One Special Identity between the complete elliptic integrals of the first and the third kind | |
| dc.type | text |