All Questions

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 ...

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(\...

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),...

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 $$ s_k = \int_{[-1,1]} x^k\,\mathrm{d}\mu,\quad \forall k\in\mathbb N\;? $$ ...