Talk:List of mathematical series

Untitled
Does anybody know the representation for $$ \sum_{n=0}^\infty z^{n^2} $$, where |z|<1?
 * It is $$\frac{1+\vartheta_3(0,z)}{2}.$$ See Abramowitz, Stegun, Handbook of Mathematical Functions, (16.27.3)--131.220.161.244 (talk) 10:47, 27 August 2009 (UTC)

Infinite sum
What's that? If a sum is infinite it's probably not even defined. Are we talking about diverging series? 213.112.76.90 (talk) 13:05, 15 May 2009 (UTC)
 * No, we talking about a sum of infinite object which convergent into a value. see also Infinite sum --77.125.107.105 (talk) 11:57, 30 August 2009 (UTC)

Confusing notation
I am probably going to change the index of summation in all the series on the page to $$m$$ -- having it as $$i$$ is probably a good source of unnecessary confusion (conflicts with $$i=\sqrt{-1}$$) tryptographer (talk) 06:17, 14 July 2010 (UTC)

Trigonometric functions
These two equations are wrong! If n is a natural number any of those two sums are in general different from zero. If n tends to infinity, the series converge, but not to zero. The sum of cosines would converge if m started on zero...

Please somebody correct me if I'm wrong, otherwise correct the article. —Preceding unsigned comment added by 193.136.104.23 (talk) 11:24, 6 September 2010 (UTC)

Proofs
What about the proofs for some of these closed forms? I there a place I'd be able to find that?

I, too, would value a reference for the closed form expressions. I can hardly name Wikipedia as a reference. — Preceding unsigned comment added by 141.211.139.138 (talk) 00:20, 8 April 2012 (UTC)

Sepating into finite series and infinite series
What do you think about separating this article into finite series and infinite series?--MathFacts (talk) 06:00, 10 November 2010 (UTC)

Finite Sum Power Series
Where did the formulas for series like $$\sum_{m=1}^n m^2 x^m = \frac{x(1+x-(n+1)^2x^n+(2n^2+2n-1)x^{n+1}-n^2x^{n+2})}{(1-x)^3} \,\!$$ come from? Is there a solution for $$\sum_{m=1}^n m^k x^m\!$$? — Preceding unsigned comment added by BenRMorin (talk • contribs) 07:52, 22 March 2011 (UTC)
 * the solution for $$\sum_{m=0}^{n-1} m^k x^m\!$$ is $$(x d/dx)^k (1-x^n)/(1-x)$$, where $$(x d/dx)^k $$ is the operator (x times derivative(x)) applied k times. --131.220.161.244 (talk) 14:48, 2 May 2012 (UTC)

Geometric Progression of 'i' i.e. S= 1+i+i²+i³+i⁴+... Upto N terms
Ubove Sum S can only have following 4 values for every N being Even Or Odd 1. S=0 2. S=i+1 3. S=i 4. S=1 No other then these sum exists. Sum upto infinity i.e. S= 1+i+i²+i³+...upto ∞ is ( i+1)/2

Above stated sum can be obtained By using following formulae

S=1+i+i²+i³+...upto N terms

S= \frac{ i+1 }{ 2  }  (1+(-1)  ^ {  \frac{ n+2  }{ 2  }    }  ) if n is Even

n is number of terms in series

S= \frac{ (-1) ^ {  \frac{ n-1  }{ 2  {    }  +(-1)  ^ {  \frac{ n+1  }{ 2  }    }  i+i+1  }{ 2  }   if n is odd And also it is the average of all the possible sum of GP of i upto N terms. NihalHanfi (talk) 09:42, 17 November 2020 (UTC)

Exponential and logarithmic sum error
Your sum (linked below?) equals ln2-1/2, not ln2.

John W. Patterson (520) 971-4614

https://wikimedia.org/api/rest_v1/media/math/render/svg/940b1790cbab3f08e97e6bbb6559c627404b1806 68.98.225.139 (talk) 22:21, 16 April 2023 (UTC)