Hypergeometric Function D.E. Solution | Near x = -1 | No Quotation Marks

zorro
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Homework Statement

Find the general solution in terms of Hypergeometric functions near x = -1 :
(1-x2)y'' - (5x2 - 9)/5x y' + 8y = 0

The Attempt at a Solution



Here the coefficient of y' contains 9/5x which causes problem. The general form contains the coefficient of y' as A+Bx

How do I solve this?
 
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Solved it.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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