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Bessel Functions

Please check out the book (Boas 12.12). For non integer p,

equation107

and

equation109

i.e., tex2html_wrap_inline313 goes to tex2html_wrap_inline315 as r goes to tex2html_wrap_inline315 , and tex2html_wrap_inline321 goes to tex2html_wrap_inline315 as r goes to zero. For integer p,

equation114

i.e., tex2html_wrap_inline313 is even for even p and odd for odd p. Check out all the nice relations Boas p. 514. Spherical Bessel Functions same as I's and K's can be found in Boas p. 517 - 518. Also:

equation117

General case Bessel Equation:

equation121

Solution:

equation131

with tex2html_wrap_inline337 . Useful relations:

equation134

where a and b are zeros of tex2html_wrap_inline345 .


Joshua Deutsch
Thu Nov 12 17:06:39 PST 1998