| 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 : '(,x.)"_ ^!.1/ i.@[' Rising factorial L1=: 2 : 'x.rf %&(*/) y.rf' L2=: (i.@[ ^~ ]) % (!@i.@[) H=: L1 (+/ . *) L2 |
'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 f=: 1 H. 1 8 f i. 6 1 2.71825 7.38095 19.8464 51.8063 128.619 f 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