  We prove that topological recursion applied to the spectral curve of colored
HOMFLY-PT polynomials of torus knots reproduces the n-point functions of a
particular partition function called the extended Ooguri-Vafa partition
function. This generalizes and refines the results of Brini-Eynard-Marino and
Borot-Eynard-Orantin.
  We also discuss how the statement of spectral curve topological recursion in
this case fits into the program of Alexandrov-Chapuy-Eynard-Harnad of
establishing the topological recursion for general weighted double Hurwitz
numbers partition functions (a.k.a. KP tau-functions of hypergeometric type).
