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2 votes
1 answer
146 views

Mellin transform (of sequences)

Is it possible to define the Mellin transform for sequences of real numbers or even for tuples? Is there any book treating this argument? Any idea or suggestion will be greatly appreciated Since the ...
MathG's user avatar
  • 131
1 vote
0 answers
103 views

Generalizion of Euler identity with infinite sum of inverse squares

For $x,y\in \mathbb{R}\backslash \mathbb{Z}$ let $$ f(x,y)=\sum_{n\in\mathbb{Z}} \frac{1}{(n-x)(n-y)} $$ Is there a closed formula for $f(x,y)$? What is known: We have $$ f(x,x)=\left(\frac{\pi}{\sin(\...
user35593's user avatar
  • 2,286
2 votes
2 answers
257 views

Reference request for function by which to compute coefficients of continued fraction of algebaic number

The simple continued fraction is in the form $$[1;1,2,3,4,5,\dots]=1+\cfrac{1}{1+\cfrac{1}{2+\cdots}}, $$ for instance. Obviously,the coefficients $x_i$can be computed by computable function $x_i=f(i),...
XL _At_Here_There's user avatar
6 votes
2 answers
445 views

Moment problem on [-1,1]: necessary and sufficient conditions

Consider a sequence of real numbers $s=(s_0,s_1,\ldots)$. When is there a Borel measure $\mu$ supported on $[-1,1]$ so that $$ s_k = \int_{[-1,1]} x^k\,\mathrm{d}\mu,\quad \forall k\in\mathbb N\;? $$ ...
MERTON's user avatar
  • 505