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Dec
17
comment Explanation of method for showing that 0 / 0 is undefined
The second equality is only true if $$x\ne(-x)$$ Zero does not satisfy this, so only the first one is correct.
Dec
9
comment Series diverging to infinity and series converging to infinity - is there a difference?
@rank no. Sequence of 1+1+1+1+... diverges to infinity. But can be summed up to -1/2. I wonder whether there are separate series about which one can say that they converge to infinity.
Dec
9
comment Why we cannot ascribe values to behavior of functions at poles?
Good point. I will think about it.
Dec
9
comment Convergence of Newton series
@Jack M since he is speaking about forward difference, it can be assumed the points are equidistant, 1-separated unless one mentions time scales.
Dec
8
comment Why we cannot ascribe values to behavior of functions at poles?
@AlexR yes, this Caushy principal value is the real part of what I propose as a value of a function in a pole point. The other part is the same, but with another sign: $$\lim_{h\to 0}\frac{f(x+h)-f(x-h)}2$$ It will not be a real number (if the function has a pole in $x$, otherwise of the function is continuous it will be zero) but can be expressed in terms of $\omega$.
Dec
8
comment Zeta and Gamma function regularization with $\omega=1/0$
@Lucian for Zeta also.
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 index variable from inside a sum?
Well, yes, but I am interested in exact relations...
Dec
2
comment What is the substitution to remove index variable from inside a sum?
@Jean-Claude Arbaut are there anywhere tables of this operator applied to elementary functions? What are the rules for dealing with this operator except linearity?
Dec
2
comment What is the substitution to remove index variable from inside a sum?
@MJD particularly, I have encountered a list of when this operator was applied to some functions involving digamma en.wikipedia.org/wiki/… and wondered if this can be re-written in form of antidifferences en.wikipedia.org/wiki/…
Dec
2
comment What is the substitution to remove index variable from inside a sum?
@MJD does it mean this linear operator cannot be expressed in terms of antidifference operator?
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!