Certianly there is a lot of reference material on series transformations: they accelerate convergence, provide analytic continuations and what not. But I have not yet seen a like presentation of product transformations. Given that there are ways to write a product as a series, and vice-versa (see this post), would it be so difficult to translate known series transformations into product transformations?(adsbygoogle = window.adsbygoogle || []).push({});

An example application would be the Riemann zeta fcn, the series definition can be analytically continued to the whole complex plane (except z=1) via some clever series manipulation + a series transformation (see this post), but has anybody ever used similar techniques to analytically continue the Euler product over primes representation of the Riemann zeta? Yeah, I know about the Hadamard Product derived using the Weierstrass formula, but that is not what I'm after.

Just fishing for your ideas,

-Ben

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# Product transformations?

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