# Simple recurrence and contextual meaning of IncludeSingularTerm = false ?

Posted 4 months ago
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 Hello, while playing with this recurrence relation: g(n+1)=10*log(n)+g(n) Wolfram Alpha produces this answer: g(n) = c_1 + 10 log(Γ(n)) (c_1 is an arbitrary parameter) (by the way, a Step-by-Step option would be great).When I simply change the sign of the LHS term, the proposed solution is instead: I have checked the generalized Riemann Zeta function documentation, and then searched the web as well, but could not get a clue about the meaning and use of:IncludeSingularTerm = FalseAny suggestion about how to proceed to gain a thorough understanding of its meaning in this context?I was hoping to get some hint from an examination of the "Open Code" output, but its generation appears to hang forever (I have a Premium Pro Subscription). Many Thanks !
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Posted 4 months ago
 Evaluating ??IncludeSingularTerm in Mathematica sheds some light: ??IncludeSingularTerm "IncludeSingularTerm is an option for LerchPhi and Zeta. With IncludeSingularTerm -> True, terms involving ((k + a)^2)^(-s/2) with k + a == 0 are included. With IncludeSingularTerm -> False, they are not." This is also mentioned in the docs of the more general Lerch transcendent, LerchPhi[] (of which Hurwitz zeta is a special case); unfortunately the docs for Zeta[] neglect to mention this setting.Evaluating Options[Zeta] {IncludeSingularTerm -> False} shows that the singular term is excluded by default: Zeta[2, -1, IncludeSingularTerm -> True] ComplexInfinity Zeta[2, -1, IncludeSingularTerm -> False] 1 + π^2/6 
Posted 4 months ago
 Thanks J.M.I then also wonder whether I am correctly interpreting the meaning of (for clarity, I have replace n/2 with n) as the following derivative with respect to the first variable, s, in a result listed at http://mathworld.wolfram.com/HurwitzZetaFunction.htmlor am I rather mistaking this particular Wolfram Alpha syntax for derivatives?
Posted 4 months ago
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