 Rational Binomial Coefficients - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: HP Prime Software Library (/forum-15.html) +--- 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