Reduce-svn5758-src/xmpl/zeilberg.rlg

152 % gosper(1/(k+1)*binomial(2*k,k)/(n-k+1)*binomial(2*n-2*k,n-k),k);
307 gosper(binomial(k,n),k);
310  (k + 1)*binomial(k,n)
314 gosper(k*binomial(k,n),k);
317  (k*n + k + n)*(k + 1)*binomial(k,n)
321 % gosper(k^10*binomial(k,n),k);
322 gosper(1/binomial(k,n),k);
327  (n - 1)*binomial(k,n)
329 gosper(k/binomial(k,n),k);
334  (n - 2)*binomial(k,n)
336 % gosper(k^10/binomial(k,n),k);
337 gosper(binomial(k-n,k),k);
340  (n - 1 - k)*binomial(k - n,k)
344 gosper((-1)^k*binomial(n,k),k);
348   - ( - 1) *(k - n)*binomial(n,k)
352 gosper((-1)^k/binomial(n,k),k);
358  (n + 2)*binomial(n,k)
381 summand:=binomial(n,k)/2^n$
387  (n + 1 - k)*(binomial(n + 1,k) - 2*binomial(n,k))
394 summand:=binomial(n,k)^2/binomial(2*n,n)$
401 ((binomial(n + 1,k) *binomial(2*n,n) - binomial(2*(n + 1),n + 1)*binomial(n,k) )
409    *binomial(2*(n + 1),n + 1)*binomial(2*n,n))
430 % summand:=(-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*binomial(b+c,b+k)*
576 gosper(binomial(A,k),k);
608 gosper(binomial(n,k),k);
619 sumrecursion(binomial(n,k),k,n);
624 sumrecursion(k*binomial(n,k),k,n);
632 % (-1)^k*binomial(2*n,k)*binomial(2*k,k)*binomial(4*n-2*k,2*n-k),k,n);
633 sumrecursion(binomial(n,k)^2,k,n);
638 sumrecursion(binomial(n,k)^2/binomial(2*n,n),k,n);
643 % sumrecursion((-1)^k*binomial(n,k)^2,k,n);
686 % sumrecursion((-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*
687 %    binomial(b+c,b+k)*
689 sumrecursion((-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*
690    binomial(b+c,b+k),k,n);
695 sumrecursion((-1)^(k-n)*binomial(2*n,k)^3,k,n);
702 (-1)^(k-n)*binomial(2*n,k)^3/(binomial(3*n,n)*binomial(2*n,n)),k,n);
722 sumrecursion(binomial(n,k)^2*binomial(n+k,k)^2,k,n);
731 % sumrecursion(4*(-1)^k*binomial(m-1,k)*binomial(2*m-1,2*k)/
732 % binomial(4*m-1,4*k)*(4*m^2+16*k^2-16*k*m+16*k-6*m+3)/
734 sumrecursion((-1)^k*binomial(n,k)*binomial(k,n),k,n);
739 sumrecursion((-1)^k*binomial(n,k)*binomial(2*k,n),k,n);
744 sumrecursion((-1)^k*binomial(n,k)*binomial(k,j)^2,k,n);
750 sumrecursion(binomial(n,k)*binomial(a,k),k,n);
755 sumrecursion((3*k-2*n)*binomial(n,k)^2*binomial(2*k,k),k,n);
760 sumrecursion(binomial(n-k,k),k,n);
765 sumrecursion(binomial(n,k)*binomial(n+k,k),k,n);
770 % sumrecursion(binomial(n+k,m+2*k)*binomial(2*k,k)*(-1)^k/(k+1),k,n);
771 sumrecursion((-1)^k*binomial(n-k,k)*binomial(n-2*k,m-k),k,n);
776 % sumrecursion((-1)^k*binomial(n-k,k)*binomial(n-2*k,m-k),k,m);
777 sumrecursion(binomial(n+k,2*k)*2^(n-k),k,n);
782 sumrecursion(binomial(n,k)*binomial(2*k,k)*(-1/4)^k,k,n);
787 % sumrecursion(binomial(n,i)*binomial(2*n,n-i),i,n);
788 sumrecursion((-1)^k*binomial(n,k)*binomial(2*k,k)*4^(n-k),k,n);
793 sumrecursion((-1)^k*binomial(n,k)/binomial(k+a,k),k,n);
798 % sumrecursion((-1)^k*binomial(n,k)/binomial(k+a,k),k,a);
799 sumrecursion((-1)^(n-k)*binomial(2*n,k)^2,k,n);
814 sumrecursion(binomial(2*n+1,2*p+2*k+1)*binomial(p+k,k),k,n);
819 % sumrecursion(binomial(2*n+1,2*p+2*k+1)*binomial(p+k,k),k,p);
820 sumrecursion(binomial(r,m)*binomial(s,t-m),m,r);
825 % sumrecursion(binomial(r,m)*binomial(s,t-m),m,s);
826 % sumrecursion(binomial(r,m)*binomial(s,t-m),m,t);
827 sumrecursion(binomial(2*n+1,2*k)*binomial(m+k,2*n),k,n);
832 % sumrecursion(binomial(2*n+1,2*k)*binomial(m+k,2*n),k,m);
833 sumrecursion(binomial(n,k)*binomial(k,j)*x^j,k,n);
838 % sumrecursion(binomial(n,k)*binomial(k,j)*x^j,k,j);
839 % sumrecursion(binomial(n,k)*binomial(k,j)*x^k,k,n);
840 sumrecursion(x*binomial(n+k,2*k)*((x^2-1)/4)^(n-k),k,n);
846 sumrecursion(binomial(n+k-1,2*k-1)*(x-1)^(2*k)*x^(n-k)/k,k,n);
853 1/(k+1)*binomial(2*k,k)/(n-k+1)*binomial(2*n-2*k,n-k),k,n);
858 sumrecursion(binomial(m,r)*binomial(n-r,n-r-q)*(t-1)^r,r,m);
865 % sumrecursion(binomial(m,r)*binomial(n-r,n-r-q)*(t-1)^r,r,n);
866 % sumrecursion(binomial(m,r)*binomial(n-r,n-r-q)*(t-1)^r,r,q);
867 % sumrecursion(binomial(m,r)*binomial(n-r,n-r-q)*(t-1)^r,r,r);
879 sumrecursion((-1)^k*binomial(n,k)^3,k,n);
889 % sumrecursion(binomial(n+k+1,n-k)*pochhammer(-n+k,j)*pochhammer(k+1/2,j)*
895 % sumrecursion(binomial(n+k+1,n-k)*pochhammer(-n+k,j)*
964 %    (-1)^n*p^n*binomial(NN,n)*hyperterm({-n,-x},{-NN},1/p,k)$
1005 extended_gosper(binomial(k/2,n),k);
1009  (k + 2)*binomial(---,n) + (k + 1)*binomial(-------,n)
1014 extended_gosper(binomial(n,k/2)-binomial(n,k/2-1),k);
1018 ( - ((2*n + 3 - k)*(n + 1 - k)*(binomial(n,-------) - binomial(n,-------))
1022       + (n + 2 - k)*(2*(n + 1) - k)*(binomial(n,-------) - binomial(n,---))))/(2
1029 % extended_sumrecursion(binomial(n,k)*binomial(k/2,n),k,n,1,2);
1030 sumrecursion(binomial(n,k)*binomial(k/2,n),k,n);
1037 extended_sumrecursion(binomial(n/2,k),k,n,2,1);
1042 sumrecursion(binomial(n/2,k),k,n);
1139 sumtohyper(binomial(n,k)^3,k);
1144 sumtohyper(binomial(n,k)/2^n-sub(n=n-1,binomial(n,k)/2^n),k);
1154 sumtohyper(binomial(k+j-1,k-j)*2*(-1)^(j+1)*factorial(2*j-1)/
1160 % term:=1/(n-1+k)*(1/2-1/2*x)^k/n*binomial(k-n-1,-n-1)*k*
1161 %         binomial(n-1+k,n-1);