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facexpand-factorial_expand-minfactorial-sum

f(k):=(2*n)!/(k!*(2*n...

facexpand: true, fact...

f(k+1)/f(k);

Calculate

facexpand-factorial_expand-minfactorial

f(k):=(2*n)!/(k!*(2*n...

facexpand: true, fact...

f(k+1)/f(k);

Calculate

facexpand-factorial_expand-minfactorial-sum

f(k):=(2*n)!/(k!*(2*n...

facexpand: true, fact...

f(k+1)/f(k);

Calculate

facexpand-factorial_expand-minfactorial-sum

f(k):=(2*n)!/(k!*(2*n...

facexpand: true, fact...

f(k+1)/f(k);

Calculate

facexpand-factorial_expand-minfactorial-sum

f(k):=(2*n)!/(k!*(2*n...

facexpand: true, fact...

f(k+1)/f(k);

Calculate

facexpand-factorial_expand-minfactorial-sum

f(k):=(2*n)!/(k!*(2*n...

facexpand: true, fact...

f(k+1)/f(k);

Calculate

facexpand

? facexpand;

Calculate

facexpand-factorial_expand-minfactorial-sum

f(k):=(2*n)!/(k!*(2*n...

facexpand: true, fact...

f(k+1)/f(k);

Calculate

facexpand-factorial_expand-minfactorial-sum

f(k):=(2*n)!/(k!*(2*n...

facexpand: true, fact...

f(k+1)/f(k);

Calculate

facexpand

? facexpand;

Calculate

facexpand

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
? facexpand;

 -- Option variable: facexpand
     Default value: `true'

     `facexpand' controls whether the irreducible factors returned by
     `factor' are in expanded (the default) or recursive (normal CRE)
     form.


(%o1)                                true
(%i2) 
Run Example
f(k):=binomial(2*n,k)*a^(2*n-k)*b^k;
                                               2 n - k  k
(%o1)                f(k) := binomial(2 n, k) a        b
(%i2) facexpand: true;
(%o2)                                true
(%i3) f(k+1)/f(k);
                            b binomial(2 n, k + 1)
(%o3)                       ----------------------
                              a binomial(2 n, k)
(%i4) eq: sum(f(kk),kk,0,n);
                     n
                    ====
                    \       2 n - kk  kk
(%o4)                >     a         b   binomial(2 n, kk)
                    /
                    ====
                    kk = 0
(%i5) 

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