Bessel functions of first kind $$J_n(z)$$: 

NB.*BesselJ a Bessel functions of first kind
BesselJ=: 1 : '(i.0) H. (1+m.)@(_0.25&*)@*: * ^&m.@-: % (!m.)"_'
J0=: 0 BesselJ
J1=: 1 BesselJ

This is obtained directly from representation of Bessel function as hypergeometric function.

Normal distribution: 

erf =: (*&(%:4p_1)%^@:*:)*[:1 H. 1.5*:    NB. A&S 7.1.21 (right)
cnd =: [:-:1:+[:erf%&(%:2)            NB. A&S 26.2.29 (solved for P)

See also

Phrases/SpecialFunctions (last edited 2008-12-08 10:45:50 by )