Path: csiph.com!x330-a1.tempe.blueboxinc.net!usenet.pasdenom.info!news.albasani.net!eternal-september.org!feeder.eternal-september.org!mx04.eternal-september.org!.POSTED!not-for-mail From: Joe Riel Newsgroups: comp.soft-sys.math.maple Subject: Re: Series Summation Question Date: Thu, 26 Jan 2012 08:21:49 -0800 Organization: A noiseless patient Spider Lines: 35 Message-ID: <87vcnywi1u.fsf@san.rr.com> References: <1fe7f908-df47-4b54-949f-630a50b0551e@j14g2000vba.googlegroups.com> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Injection-Info: mx04.eternal-september.org; posting-host="fkgjSOZ+03w83W7QjZBmIg"; logging-data="3244"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/6+36yQ538++rWlpYSCkP6" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/23.3 (gnu/linux) Cancel-Lock: sha1:ek+S1RdowvkrZZZzNR0dbcjJ5+0= sha1:vctdhgm1Iuuz/CgbgWK6ULQyqQA= Xref: x330-a1.tempe.blueboxinc.net comp.soft-sys.math.maple:332 clashton writes: > I am a little curious about whether Maple can evaluate a certain > infinite sum that fails with Mathematica (I do not have Maple so > cannot test it myself). > > Here is the sum in Mathematica: > Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, Infinity}] /. {q -> 0.1} > This leads to and error, > but > (Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, 1}] /. {q -> 0.1) > + > (Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 2, Infinity}] /. {q -> 0.1}) > gives the correct answer, which I find a little strange. > > How does Maple perform on the original sum? Summing numerically (and guessing at the meaning of the Mathematica): (**) S := Sum(q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), n=0..infinity); infinity ----- (-6 + 4 n) \ q S := ) --------------- / (-5 + 4 n) ----- 1 - q n = 0 (**) evalf(eval(S,q=1/10)); -21.10120010 -- Joe Riel