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Unformatted text preview: Phgsics 325, Fall 2006 Solutions to Homework Assignment #I i) Taylor expansion of erf (r) : # f; e"u'du. we need the first three nonzero terms, e v a i u a t e d a t r : 0 . erf(0) : g erf'  rtu:" by the fundamental theorem of calculus. erf, : h u, r : 0. erf't = rtlZr""] which vanishes at c:0, er.ft" : hlr"n + 4rr","1which hasthe value ff at r : 0. erfrrrt  ftl+re,' *8xe,2  Brt",'l which ,runi.n", at r = 0. :: {""' ;,k [tle" + 4e" + Be,'' I6r2e,'  24rze,' * r6rae,rl which has r]re v a l u e # a t r : 0 . The firit three nonzero terms of the Taylor expansion are e r f ( r ) = o * h * o  # + o + m Hete's an elegant alternative solution (easier, tool). you can express eu, : Ino g#f , and integrate that ,:l.,T,l{,t.rm to get a series expansion for eri(x). erf(x):rtDy)ffi Reading off the first'three terms gives e r f ( r ) = * 1 "  4 + t l l Which agrbes' with it . u"U'ou....
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This note was uploaded on 02/23/2009 for the course PHYS 325 taught by Professor Lamb during the Fall '09 term at University of Illinois at Urbana–Champaign.
 Fall '09
 Lamb
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