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minfactorial

f(n):=(b+n)!/(a+n)!;

f(n+1)/f(n);

minfactorial(f(n+1)/f...

Calculate

minfactorial

? minfactorial;

Calculate

minfactorial

n!/(n+2)!;

minfactorial (%);

Calculate

minfactorial

f(n):=(b+n)!/(a+n)!;

f(n+1)/f(n);

minfactorial(f(n+1)/f...

Calculate

minfactorial

? minfactorial;

Calculate

minfactorial

n!/(n+2)!;

minfactorial (%);

Calculate

minfactorial

Run Example
(%i1)f(k):=(2*n)!/(k!*(2*n-k)!)*a^(2*n-k)*b^k;
                                  (2 n)!      2 n - k  k
(%o1)                  f(k) := ------------- a        b
                               k! (2 n - k)!
(%i2) facexpand: true, factorial_expand: true;
(%o2)                                true
(%i3) f(k+1)/f(k);
                                b k! (2 n - k)!
(%o3)                      -------------------------
                           a (k + 1)! (2 n - k - 1)!
(%i4) minfactorial(f(k+1)/f(k));
                                  b (2 n - k)
(%o4)                             -----------
                                   a (k + 1)
(%i5) eq: sum(f(kk),kk,0,n);
                                 n
                                ====     2 n - kk  kk
                                \       a         b
(%o5)                    (2 n)!  >     ---------------
                                /      kk! (2 n - kk)!
                                ====
                                kk = 0
(%i6) solve_rec();
(%o6)                             solve_rec()
(%i7) 
Run Example
f(j):=binomial(k,j)*3^(k-j)*gamma(k/2+j+a)/gamma(k/2+j);
                                        k - j       k
                        binomial(k, j) 3      gamma(- + j + a)
                                                    2
(%o1)           f(j) := --------------------------------------
                                           k
                                     gamma(- + j)
                                           2
(%i2) minfactorial(makefact(f(j+1)/f(j)));
                               k
                              (- + j + a) (k - j)
                               2
(%o2)                         -------------------
                                          k
                               3 (j + 1) (- + j)
                                          2
(%i3) 
Run Example
n:3;
(%o1)                                  3
(%i2) minfactorial(subst(0,x,makelist(diff(1/(1-4*x)^(k/2),x,ii),ii,1,n)));
                            k               k         k
(%o2)          [2 k, - 8 (- - - 1) k, 32 (- - - 2) (- - - 1) k]
                            2               2         2
(%i3) makelist(1/4^ii*Gamma(k/2+ii)/Gamma(k/2),ii,1,n);
                         k             k             k
                   Gamma(- + 1)  Gamma(- + 2)  Gamma(- + 3)
                         2             2             2
(%o3)             [------------, ------------, ------------]
                            k             k             k
                    4 Gamma(-)   16 Gamma(-)   64 Gamma(-)
                            2             2             2
(%i4) 

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