ChapterH2n

H2n

Hankel function of the second kind, order n.

Loading LOADSUB ALL FROM "BESRC.HTS"

or LOADSUB FROM "MATHLIB.HTS"

Usage INTEGER N

REAL X

COMPLEX C

C=FNH2n(N,X)

Description

FNH2n returns the value of the Hankel function of the second kind and order n of x, Hn(2)(x). For positive values of x, the real component of the value returned contains Jn(x) and the imaginary component contains Yn(x). For negative values of x, the real component contains (-1)n+13Jn(x) and the imaginary component of C contains (-1)n+1Yn(x).

Errors

FNH2n causes an HTBasic error if its arguments are not of the types shown in the USAGE section, above. It also causes an error if the value of x is near zero, since the imaginary component of Hn(2)(0) is infinite.

See Also

H1n, H20, H21, J0, J1, Y0, Y1

Note

The algorithm used computes the value of Hn(2) using a recursion from the values of H0(2) and H1(2). The computation time increases with n and the computation accuracy decreases with n.

Hn(2)(x)

Arg[Hn(2)(x)], degrees