0

I was asking myself... What relationship is there,what have they in common Bessel, Hankel and Legendre functions?..in terms of Helmholtz equations.

alb084
  • 1
  • Hi, welcome to the site! Perhaps it would be helpful if you could clarify your question so that we know exactly what you're looking for. For example, are you interested in comparing specific properties of these functions? And what do you mean by "better"? Maybe you're solving PDEs (e.g. Laplace's equation or Helmholtz's equation), using separation of variables in different coordinate systems, and you're wondering how you know which of the special functions should be used in each case to construct the solution to the PDE? – Kenny Wong May 15 '17 at 15:21
  • Hi :). I'm studyng an argument about acoustic field end than there are varius example with only analitics form....since that any problem in "terms of spherical function" use both to find the same solution...i'm asking myself wich was better from another. "you're wondering how you know which of the special functions should be used in each case?"...........yes i think that the question be properly this. – alb084 May 15 '17 at 15:28
  • I'm terribly sorry but I don't understand what you are asking, so I cannot help you. I hope you get a useful answer from someone else! – Kenny Wong May 15 '17 at 15:33
  • sorry...surely for my bad english...but it's not easy explain this think... the argument that i'm studyng is : Equations and their Solutions...end since that formally any solution of this special function allow me to resolve an equations for studyng an wave propagation in a field....i wonder myself...if there any function have the same purpose...why i've to choose for example bessel rather than hankel?...i hope that this time i've made it clear.... – alb084 May 15 '17 at 15:56
  • The general solution to the Helmholtz equation can be written in terms of Bessel functions in cylindrical coordinates, or in terms of Legendre polynomials in spherical coordinates. Both forms of the general solution contain unknown constants, which are to be determined by imposing boundary conditions. It is here that it may be advantageous to work with one form of the general solution rather than the other. For example, if the boundary conditions have cylindrical symmetry, it would be more convenient to determine the unknown coefficients in the solution with cylindrical coordinates. – Kenny Wong May 15 '17 at 19:20
  • Spherical Bessel functions are Fourier transform of Legendre polynomials. – Machinato Sep 09 '20 at 19:38

0 Answers0