Expand of the Bessel functions when the order is integer
Subject: Expand of the Bessel functions when the order is integer
From: Richard Fateman
Date: Wed, 02 Nov 2011 14:17:20 -0700
On 11/2/2011 3:33 AM, Aleksas Domarkas wrote:
> Expand of the Bessel functions when the order is integer
>
> "besselexpand:true" not affect when the order is integer
>
> How expand
> bessel_j(2,x) to (2*bessel_j(1,x)-bessel_j(0,x)*x)/x
> bessel_j(3,x) to
> -(-8*bessel_j(1,x)+4*bessel_j(0,x)*x+bessel_j(1,x)*x^2)/x^2
> bessel_j(2,2) to bessel_j(1,2)-bessel_j(0,2)
> bessel_j(3,2) to bessel_j(1,2)-2*bessel_j(0,2)
> bessel_j(4,2) to 2*bessel_j(1,2)-5*bessel_j(0,2) ?
>
> How simplify
> -bessel_y(6,2)*bessel_j(7,2)+bessel_y(7,2)*bessel_j(6,2)
> to
> bessel_y(1,2)*bessel_j(0,2)-bessel_y(0,2)*bessel_j(1,2) ?
>
> Aleksas D
>
>
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b[n](x):=2*b[n-1](x)-b[n-2](x)$
b[0](x):=bessel_j(0,x);
b[1](x):=bessel_j(1,x);
try b[2](2).
or ratsimp(b[3](x)), which is different from your answer.
RJF