-
[section:sph_bessel Spherical Bessel Functions of the First and Second Kinds]
[h4 Synopsis]
The functions __sph_bessel and __sph_neumann return the result of the
Spherical Bessel functions of the first and second kinds respectively:
-sph_bessel(v, x) = j[sub v](x)
+[:sph_bessel(v, x) = j[sub v](x)]
-sph_neumann(v, x) = y[sub v](x) = n[sub v](x)
+[:sph_neumann(v, x) = y[sub v](x) = n[sub v](x)]
where:
The functions return the result of __domain_error whenever the result is
undefined or complex: this occurs when `x < 0`.
-The j[sub v][space] function is cyclic like J[sub v][space] but differs
-in its behaviour at the origin:
+The j[sub v] function is cyclic like J[sub v] but differs in its behaviour at the origin:
[graph sph_bessel]
-Likewise y[sub v][space] is also cyclic for large x, but tends to -[infin][space]
+Likewise y[sub v] is also cyclic for large x, but tends to -[infin]
for small /x/:
[graph sph_neumann]
The special cases occur for:
-j[sub 0][space]= __sinc_pi(x) = sin(x) / x
+[:j[sub 0]= __sinc_pi(x) = sin(x) / x]
and for small ['x < 1], we can use the series:
which neatly avoids the problem of calculating 0/0 that can occur with the
main definition as x [rarr] 0.
-[endsect]
+[endsect] [/section:sph_bessel Spherical Bessel Functions of the First and Second Kinds]
[/
Copyright 2006 John Maddock, Paul A. Bristow and Xiaogang Zhang.