By Hall E. H.
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Extra info for A Theory of the Hall Effect and the Related Effect for Several Metals
V \ &y d) [tt t"t tk. )_5(J/)(Q+ th)] dt. -~ I\v as e II) V+-I B,tt)~ s:/ tQ,+<'~tt)h)dtt t-)V! kII \ o tV) tV) Bvtb[t tti-th)-! 43} We can rewrite Theorem 6 in an analogous manner. (.. ·. and IA (. vh,v ~l By (t)ttQ+th)dt, + (-) '/! Y+'I it being assumed here that equalities \I:l,~, ... '\fh,; the arbitrary e and t'I Q 1 l,I-t >_. 44} 91 need only satisfy the in- 32 V. M. " IIoH \ ~yd)t;. f(II)(a.... 44): a.. ,+911,)+ ) V~ MI h/ \ 0. Uy (j) lltlH wAh,) dt ... 46) into one, namely, (provided that we have Q,+ h,e > \A,).
Be a function that is analytic in the complex plane with the exception of the set of singularities. Then, for n,:4,'l, ... A! +~Al,)= Ht) 't.. 'X,)J+ . ;- n.. ~ x. , and the numbers Q" by condition ~ \ leI, lEHl\ (mM1. f:JL 0 f the s tr a i g h t Ii n e j 0 i n i n g t h P. , t-Q. t Proof. 8 ) AX, with L = 0, i , ... , 111 and the integrals on the right-hand side are taken over the segment of the straight line joining the points~;. 2). 2) that the points 'ti. §olt). +iA't.. H : t " to . :. ,~.
R em ark. 23) or G ~I R,y:~-/'i\ 5y ·Utld'\t)dt ... 25) Lemma 6. u.. ~ H~) . \ l-) ~ ~9) f 'J - n (~+e).. d. ) ~ + ' [ . ej)t l-~ ~e J=l J. V. e f\ lb t lV) (X,+ t) dt. KALININ Proof. 9 >u,. 26) to Here, the first sum on the right-hand side is a part of a Taylor's series of the function 'l:,T9·1oI '! 9) J. =""', • n ... / \I , :t ..... , we have ~ =a -0. 26). Theorem 6. ~. , ... 28) SPECIAL FUNCTIONS AND LIMIT PROPERTIES OF PROBABILITY DISTRIBUTIONS 29 Proof. 28). R em ark 1. 28) of Theorem 6 can also be written in several different ways.
A Theory of the Hall Effect and the Related Effect for Several Metals by Hall E. H.