Sunday, January 03, 2021

[gkmzuulc] functions with infinite roots

the Weierstrass factorization theorem allows constructing an entire function by specifying all its roots (and their multiplicities), up to an infinite number of roots.

consider the function whose roots are evenly spaced points along an Archimedean spiral in the complex plane.  or Ulam spiral.

can these functions be computed efficiently?  the summation of the Weierstrass factorization theorem suggests an evaluation method.  do roots have declining effect by distance?

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