. The Bell System technical journal . A A G Fig. 2—Deformation of contour in w plane. Using this deformation of the contour we may write equation (2)as follows: ^ (1 - T-)r\ I ~ I ~ J (w~- \yi- ^ > I- Jkils Jkiis Jk^ls ^ r{w- — \y- (1+) gixrw^d^ with the understanding that arg w — 1 and arg w -\- \ have theirprincipal values at the beginning of each integration. Upon referringto (2) we see that the middle integral is — ni(r, 0) and hence TIi(r, 0) = - iLih) - Lihn where L{kO 2r{\ - r)•(1+) e^wdw ^ (isr) r^^+> w+^dw {w- - ly- (15) (16) and L{k2) is obtained from L(ki) by interchanging ki

---

. The Bell System technical journal . A A G Fig. 2—Deformation of contour in w plane. Using this deformation of the contour we may write equation (2)as follows: ^ (1 - T-)r\ I ~ I ~ J (w~- \yi- ^ > I- Jkils Jkiis Jk^ls ^ r{w- — \y- (1+) gixrw^d^ with the understanding that arg w — 1 and arg w -\- \ have theirprincipal values at the beginning of each integration. Upon referringto (2) we see that the middle integral is — ni(r, 0) and hence TIi(r, 0) = - iLih) - Lihn where L{kO 2r{\ - r)•(1+) e^wdw ^ (isr) r^^+> w+^dw {w- - ly- (15) (16) and L{k2) is obtained from L(ki) by interchanging ki and w- — 1 = T-(l — t), or sw — kl^J]. — ts~jk-f, then .(1+) ^n^idw h / kiY f^+[(l - (5-///^2-)]- tJkils (7t2 - 1)3/2 2^1 \ 5 Jo (1 - ty^^ dt = 2^(-^\ F{\, -n/2;\/2;syk,), (17) where it is understood that at the initial point of the contour 108 BELL SYSTEM TECHNICAL JOURNAL arg (1 — /) = 0, arg (1 — {s^lkr)t) = 0. This may be verified byexpanding the numerator of the integrand and using I. + /. ■, J. ,.

---

Size: 2176px × 1149px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No

Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1