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Dec
8
comment Zeta and Gamma function regularization with $\omega=1/0$
@Antonio Vargas there was a typo in the formula, sorry (actually I inserted the wrong formula).
Dec
8
comment Zeta and Gamma function regularization with $\omega=1/0$
Why the downvotes?
Dec
3
comment Can derivative of Hurwitz Zeta be expressed in Hurwitz Zeta?
@O.L. I would be OK even if it deals with a particular $q$.
Dec
2
comment What is the substitution to remove integration limit from inside an integral?
Thanks! But actually I need the solution for the sum, I just thought it is the same as for the integral...
Nov
19
comment Is there a continuous function on R such that $f(f(x))=e^{-x}$?
This is only if f required to be real-valued. If it is allowed being complex-valued (but continuous and defined on R), it can exist.
Nov
19
comment Is there exact formula that returns minimal period of a periodic function?
@Travis yes, infimum of all positive periods. Ideally. But if it worked only for non-constant analytic functions, it would be ok.
Nov
19
comment Is there exact formula that returns minimal period of a periodic function?
@GEdgar I want a formula(expression) representation, that would give it for arbitrary analytic function. Like a limit, series, integral, sum etc.
Nov
19
comment Is there exact formula that returns minimal period of a periodic function?
@Travis for such functions the formula ideally would return $0$ like for constants. But I would be satisfied if the formula worked for only analytic functions.
Nov
19
comment Is this similarity just a coincidence?
@alex.jordan digamma is indefinite sum of 1/x if u prefer en.wikipedia.org/wiki/…
Nov
17
comment How to take this integral?
@Ron Gordon typo due to a bug in Mathematica! It puts the argument before the function when copying!
Nov
9
comment Ascribing values to Gamma of negative integers
@Claude Leibovici Numerator for non-Eurer-Masceroni part is Wolstenholme numbers (A001008), denomenator is A102928 multiplyed by factorial.
Oct
31
comment Ascribing values to Gamma of negative integers
@Lucian This InverseFourierTransform[FourierTransform[f[t], t, w] (-I w)^x, w, 1] gives Cos[Pi x]Gamma[1+x] in Mathematica. Now try 0, -1, -2, -3 for x and find Gamma[1+x] from here.
Oct
31
comment Ascribing values to Gamma of negative integers
@Lucian where they need it to be infinite?
Oct
31
comment Ascribing values to Gamma of negative integers
@Lucian "require those values to be infinite" - what applications?
Oct
31
comment Ascribing values to Gamma of negative integers
@Claude Leibovici $$-\frac{((1/f))'')^2}{2(1/f)'}$$
Oct
31
comment How to express this operator through derivetives?
$$-2\frac {-(f(x))^2-f(x)f''(x)h^2+(f'(x))^2h^2}{2f(x)+f''(x)h^2}$$
Oct
31
comment How to express this operator through derivetives?
Is there a common name for this operator (from your answer)? It seems it is constant for logarithm.
Oct
31
comment How to express this operator through derivetives?
Can u please write the final result with $f(x)\ne0$ if it is not that difficult?
Oct
31
comment How to express this operator through derivetives?
how would it look like? Sorry, I do not see where u assumed this.
Oct
31
comment How to express this operator through derivetives?
Works! Except in non-pole points it does not give the original function, but this is even better. Also often need to use lomit on the quotinent.