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Math Help - Convergent power series of (x^2)-(c^2)?

  1. #1
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    Convergent power series of (x^2)-(c^2)?

    Hi,
    I'm basically trying to understand why x=0 is a regular singular point of bessels equation order c.

    I get up to:
    x^2*q(x)= (x^2-c^2)
    but my lecturer said you must show it as a convergent power series.
    I can take a limit of x-->0 thus showing its analytic but I can't obtain the series.

    Any help appreciated
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  2. #2
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    Quote Originally Posted by Roland25 View Post
    Hi,
    I'm basically trying to understand why x=0 is a regular singular point of bessels equation order c.

    I get up to:
    x^2*q(x)= (x^2-c^2)
    but my lecturer said you must show it as a convergent power series.
    Show [b]what[b] "as a convergent power series"? x^2- c^2 is itself a trivially "convergent" power series since all coefficients of powers above 2 are 0.

    I can take a limit of x-->0 thus showing its analytic but I can't obtain the series.

    Any help appreciated
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