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+--- Thread: Rational Binomial Coefficients (/thread-12074.html)
Rational Binomial Coefficients - Eddie W. Shore - 01-03-2019 05:52 AM
Introduction
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
Code:
EXPORT RATBIN(p,n)
BEGIN
// 2018-12-26 EWS
// p-q, n
// Rational Binomial Coefficient
LOCAL X;
IF n==0 THEN
RETURN 1;
ELSE
IF n==1 THEN
RETURN p;
ELSE
RETURN QPI(ΠLIST(p-MAKELIST(X,X,0,n-1))/n!);
END;
END;
END;* Note: the result is not always a fraction, but you can convert the answer to fraction by pressing [ a b/c ]
Blog Link: https://edspi31415.blogspot.com/2019/01/hp-prime-and-casio-fx-5800p-rational.html
Examples:
b_2(1/2) = -1/8
b_3(1/2) = 1/16
b_4(1/2) = -5/128
b_5(1/2) = 7/256
Source:
Henrici, Peter. Computational Analysis With the HP-25 Calculator A Wiley-Interscience Publication. John Wiley & Sons: New York 1977 . ISBN 0-471-02938-6
RE: Rational Binomial Coefficients - Thomas Klemm - 01-03-2019 08:05 AM
(01-03-2019 05:52 AM)Eddie W. Shore Wrote: There are algorithms, but the program RATBIN uses the definition.
With the HP-15C we can use:
\(\binom{p}{n}=\frac{p!}{n!(p-n)!}\)
Code:
001- 42 0 x!
002- 34 x<>y
003- 43 36 LSTx
004- 34 x<>y
005- 42 0 x!
006- 34 x<>y
007- 43 36 LSTx
008- 30 -
009- 42 0 x!
010- 20 ×
011- 10 ÷Examples:
2 ENTER 0.5 R/S
-0.1250
3 ENTER 0.5 R/S
0.0625
4 ENTER 0.5 R/S
-0.0391
5 ENTER 0.5 R/S
0.0273
Cheers
Thomas