FERROMAGNETIC DISTORTION OF A WAVE 

 B — iJLoP COS pt + fjLoQ COS qt 



+ pPiP + (2) i: (^2m + kA2n.+2) COS [(w + l);/? - mq^t 



7)1=0 



+ I'PCP + <2) r (kA2,n + ^2^+2) COS [7w/> - (m + l)g]/ 



337 



TO= — 00 7l = — 00 



X sin [_mp + /t(/]^ 

 00 00 



— i^Q"^ E 51 (^m, n-2 — 2^,„„ + yl,„, n+2) 



vi = — x re= — 00 



X sin [mp + wg]^ 



CC (JO 



+ 2vPQ X/ X, (-^TO+l, n-1 ~ -<4to+1, n+1 



m= — x n = — cc 



(22) 



+ ylm-i, n+i — Am-i, n-i) sin [w/) + wg]/^ 



with the understanding that A,., = ior r < and for r = 0, 5 < 0. 

 The first Hne is the Hnear portion of the induction, given by a perme- 

 abiUty constant at its initial value; the first two summations arise 

 from the variation of the permeability with the maximum magnetizing 

 force; the remaining terms comprise the results of distortion attrib- 

 utable to hysteresis per se. The coefficients of the induction, Cmn and 

 dmn of equation (4), may now be evaluated by selecting the necessary 

 quantities from equation (22). 



General expressions for the coefficients can be evolved in series 

 known as hypergeometric functions. These are all of the type 



F(«, ^;7;2) - 1+— j-,+ ^^TTpT) 2"!+'"'' ^^^^ 



a particular one is chosen by specifying the parameters. The coef- 

 ficients needed here are 



r ( ^^^\ K' 



A — 



V{n + 1) r 



+ 1 



F 



m -\- n 71 — m 



;« + 1;kM (24) 



for m and n both positive and m -\- n odd, and 



r(l±i 



A. = ^ 



^1" 



r(r? + i)r 



+ 1 



^( ^^,^^-^;^ + i;'^iM (25) 



