| Hypergeometric | m H. n 0 0 0 |
|
The conjunction H. applies to two numeric lists to produce
a monad which is the hypergeometric function defined in
Section 15 of Abramowitz and Stegun [13];
it is the limit of the dyadic case, whose left argument restricts
the number of terms of the approximating series. As discussed in Iverson [14], the conjunction is defined as follows: rf=: 1 : '(,m) ^!.1/ i.@[' NB. Rising factorial L1=: 2 : 'm rf %&(*/) n rf' L2=: (i.@[ ^~ ]) % !@i.@[ H =: 2 : '(m L1 n +/ . * L2) " 0' |
'a b'=: 2 3 5; 6 5 a L1 b (2 3 5 ^!.1/ i.@[) %&(*/) 6 5 ^!.1/ i.@[ t=: 4 [ z=: 7 t a L1 b z 1 1 1.71429 4.28571 t (a H b , a H. b) z 295 295 8 (1 H. 1) i. 6 1 2.71825 7.38095 19.8464 51.8063 128.619 (1 H. 1) i. 6 1 2.71828 7.38906 20.0855 54.5982 148.413 ^ i. 6 1 2.71828 7.38906 20.0855 54.5982 148.413 erf =: (1 H. 1.5)@*: * 2p_0.5&* % ^@:*: NB. error function n01cdf=: -: @: >: @: erf @: ((%:0.5)&*) NB. CDF of normal 0,1 erf 0.5 1 1.5 0.5205 0.842701 0.966105 n01cdf _2 _1.5 _1 _0.5 0 0.5 1 1.5 2 0.0227501 0.0668072 0.158655 0.308538 0.5 0.691462 0.841345 0.933193 0.97725