Let p be a rational fraction, p = num/dem. The rational binomial coefficients of order n are defined by:
B_0(p) = 1
B_n(p) = COMB(p, n) = ( p * (p – 1) * (p – 2) * (p – 3) * … * (p – n + 1) ) / n!
There are algorithms, but the program RATBIN uses the definition.
HP Prime Program RATBIN
Arguments: rational fraction, order
// 2018-12-26 EWS
// p-q, n
// Rational Binomial Coefficient
IF n==0 THEN
IF n==1 THEN
* Note: the result is not always a fraction, but you can convert the answer to fraction by pressing [ a b/c ]
Casio fx-5800p Program RATBIN
For fractional results, use the fraction button [ / ].
“FRACTION”? → P
“ORDER?” → N
Prod (P-Seq(X,X,0,N-1,1)) ÷ N! → Q
b_2(1/2) = -1/8
b_3(1/2) = 1/16
b_4(1/2) = -5/128
b_5(1/2) = 7/256
Henrici, Peter. Computational Analysis With the HP-25 Calculator A Wiley-Interscience Publication. John Wiley & Sons: New York 1977 . ISBN 0-471-02938-6
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. Please contact the author if you have questions.