**HP Prime and Casio fx-5800p: Rational Binomial Coefficients**

**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

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 ]

**Casio fx-5800p Program RATBIN**

For fractional results, use the fraction button [ []/[] ].

"2018-12-26 EWS"

"FRACTION"? → P

"ORDER?" → N

If N=0

Then

0

IfEnd

If N=1

Then

1

IfEnd

If N>1

Then

Prod (P-Seq(X,X,0,N-1,1)) ÷ N! → Q

Q

IfEnd

**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

Eddie

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.

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