Phrases/SpecialFunctions
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Bessel functions
Bessel functions of first kind :
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)
Log Gamma
lnG=:((%~ (%12 _360 1260 _1680)&p.@*:@%) + (-:^.2p1)+ ]-~ ^. * -&0.5)`(^.@!)@.(<&166)">
Translated directly from [Abramovitz, Stegun]