Special functions

• How to Differentiate Bessel Functions
  Differentiate Bessel functions using recurrence identities, with formulas for J, Y, I, and K and a worked example involving a weighted function.
• How to Derive Bessel Function Recurrences from the Generating Function
  Differentiate the Laurent generating function for J_n(x), match coefficients, and obtain the standard order and derivative recurrences.
• How to Derive the Hermite Polynomial Derivative Relation
  Differentiate the physicists’ Hermite equation to show H_n' solves the degree-(n−1) equation, then compare leading coefficients to get H_n'=2nH_{n−1}.