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I'm studying for my diff/eq final, and I am having a lot of trouble understanding the answer to a question involving Bessel's equation of order 3/2. So, here's the question. please help::::::

The following question concerns Bessel's Equation:

[tex]x^2y''+xy'+(x^2-(\frac{3}{2})^2)y=0[/tex]

The Bessel Function [tex]J_{3/2}(x)[/tex] is the Frobenius series solution which is finite at x = 0 Find the first three terms in its series expansion around x = 0.

Ok, so I have the definition of the Bessel Function as:

[tex]J_r(x)=\sum_{n=0}^{\infty} a_nx^{n+r}, a_0=1[/tex]

where 'r' is the root of the indicial equation:

[tex]r(r-1)+(1)r-(\frac{3}{2})^2[/tex]

The answer to this question says::

[tex]J_{3/2}=x^{3/2}(a_0+a_1x+a_2x^2+a_3x^3+...)[/tex]

[tex]y=x^{3/2}(1+0x-\frac{1}{10}x^2+0x^3+...)[/tex]

I don't know how they changed the [tex]a_0,a_1,a_2,...[/tex] values to those numbers right there.

Thanks for the help.

-Mark

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# Homework Help: Bessel's Eq. of order 0 and solution help

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