please please can someone hep me on this as i dont have a clue where to start. I know its a ,ong question but if someone coul do itthen would really give me a bse to understand the topic

thanks loads

Edgar

Show that Jn(px) satisfies

x^2y'' + xy' + (p^2x^2 - n^2)y = 0;

and deduce

[x d/dx Jn(px)] (Subscript)x + ((p^2)x -n^2/x) Jn(px) = 0:

Show that the integral between l and 0 of xJn(px)Jn(qx) dx =

l/(q^2 - p^2) [pJn(ql)J'n(pl) - qJn(pl)J'n(ql)] ;

and, using l'Hopital's rule,

the integral between l and 0 of

xJn^2(px) dx =l^2/2 Jn'^2(pl) + 1 - (n^2/p^2l^2)Jn^2(pl)

Deduce that, if l is such that Jn(pl), Jn(ql) are both zero (i.e. pl and ql are both

roots of Jn(x)), then

the integarl between l and 0 of

xJn(px)Jn(qx) dx = 0; p doesnt equal q