How can I learn special functions and differential equation

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SUMMARY

The discussion focuses on the challenges of learning special functions and differential equations, specifically mentioning Legendre Functions, Spherical Harmonic Functions, Bessel Functions, and others. The participants highlight the importance of these functions in applications such as Electrodynamics and Quantum Mechanics. Two key references recommended for mastering these topics are "Handbook of Mathematical Functions" by M. Abramowitz and I. A. Stegun, and "An Atlas of Functions" by J. Spanier and K. B. Oldham. Additionally, a compendium titled "Safari au pays des fonctions spéciales" is suggested for French readers, which includes a bibliography and summaries of useful special functions.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with special functions in mathematics
  • Basic knowledge of Electrodynamics and Quantum Mechanics
  • Access to mathematical reference materials
NEXT STEPS
  • Study "Handbook of Mathematical Functions" by M. Abramowitz and I. A. Stegun
  • Explore "An Atlas of Functions" by J. Spanier and K. B. Oldham
  • Review "Safari au pays des fonctions spéciales" for additional insights
  • Practice solving ordinary and partial differential equations using special functions
USEFUL FOR

Students and researchers in mathematics, physics, and engineering who are looking to deepen their understanding of special functions and their applications in differential equations.

Karmerlo
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Legendre Functions, Spherical Harmonic Functions, Bessel Functions, Neumann Functions, Airy Functions, Confluent Hypergeometric Functions, Laguerre Functions, Hermitte Functions...

I find this learning is so tedious, traumatic, and miserable. I find it so difficult to manage.
But I have to manage it, since there are wide applications in physics (Electrodynamics,Quantum Mechanics, when working on various sorts of ordinary/partial differential equation, when working on moment expansion) of such "good stuffs".

Do anyone have some very good reference (easy to find in campus lib.) can help me learn this?

Or any good suggestions to do this?
Thanks.
 
Physics news on Phys.org
Hi !
I suggest two very valuable books :

M.Abramowitz, I.A.Stegun, "Handbook of Mathematical Functions", Dover Publications, N.-Y., 1972

J.Spanier, K.B.Oldham, "An Atlas of Functions", Hemisphere Pubishing Corporation, Springer-Verlag, 1987. (There is a more recent edition)

For French readers, a compendium about the use of special functions :
"Safari au pays des fonctions spéciales"
http://www.scribd.com/JJacquelin/documents
A bibliography is provided page 11 and a summary of the most usefull special functions pp.12-17
 
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