The Net Advance of Physics:
SPECIAL FUNCTIONS

SPECIAL FUNCTIONS

• General:
  • A short-course on orthogonal polynomials and special functions by J. Petronilho [2021/11]

• Type: BERNOULLI:
  • Lecture Notes, Bernoulli Polynomials and Applications by Omran Kouba [2013/09]

• Type: BESSEL:
  • A Physicist's Guide to Explicit Summation Formulas Involving Zeros of Bessel Functions and Related Spectral Sums by Denis S. Grebenkov [2019/04]

• Type: CHEBYSHEV:
  • Properties of Chebyshev polynomials by N. Karjanto [2020/02]

• Type: EXPONENTIAL-INTEGRAL:
  • Useful Review on the Exponential-Integral Special Function by Enrico Masina [2019/07]

• Type: HEUN:
  • Heun Functions and their uses in Physics by M. Hortacsu [2011/01]
• Type: HEUN: Subtypes:
  • Coulomb Spheroidal:
  • Lamé:
  • Mathieu:

• Type: HYPERGEOMETRIC:
  • Hypergeometric Functions I by Ian G. Macdonald [ca. 1988]
  • Elliptic Hypergeometric Functions by Hjalmar Rosengren [2016/07] Lecture notes for a course.
  • A physicist's guide to the solution of Kummer's equation and confluent hypergeometric functions by W. N. Mathews Jr. et al. [2021/11]

• Type: LAMBERT W:
  • The Strange Properties of the Infinite Power Tower by Luca Moroni [2019/08]

• Type: SPHERICAL HARMONICS:
  • Spherical Harmonics in p Dimensions by Christopher Frye and Costas J. Efthimiou [2012/05]
  • Spherical Harmonics [in d-Dimensions] by Feng Dai and Yuan Xu [2013/04]

• Type: TETRATION:
  • The Strange Properties of the Infinite Power Tower by Luca Moroni [2019/08]

• Re: GROUP THEORY:
  • An Overview of the Relationship between Group Theory and Representation Theory to the Special Functions in Mathematical Physics by Ryan D. Wasson and Robert Gilmore [2013/09] For (advanced) undergraduates.

• Re: SPECTRAL THEORY: Koelink 2001/07;

THE NET ADVANCE OF PHYSICS