Special differential equation (Legendre)

Hoaky

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Mar 12, 2020
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Hey, I need some help with understanding special differential equations. I'm doing a course right now and the material given by the teacher is unclear. I've done research, but nothing clearer came up. I would like some help and context regarding Legendre associated equations and also how to transform a differential equation into an equation of a known form (such as Bessel and such).

The way to transform these equations is by changing a variable and do some otherworldly function swap which I do not understand (lack of material to practice upon).

Anyone could point me to some resources that may help me ? I've already gone through a few volumes (Greenberg and Kreisig) and I haven't found what I need.

Internet pointed me towards similar explanation to those I've been given regarding the Legendre associated equations, but I still have trouble understanding the point of deriving the equation to obtain another one. I can't seem to bridge things together even though I follow a demonstration step by step.

I know I should go see my teacher, but he's hard to get a hold of and is really bad at explaining the material.

Thank you for your help.
 
It's not at all clear what you are asking! Do you know the definitions of "Legendre" and "Bessel" equations? Can you give an example of the kind of problem you are trying to solve?
 
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