packages/sum/zeilberg.tst

44 % gosper(1/(k+1)*binomial(2*k,k)/(n-k+1)*binomial(2*n-2*k,n-k),k);
70 gosper(binomial(k,n),k);
71 gosper(k*binomial(k,n),k);
72 % gosper(k^10*binomial(k,n),k);
73 gosper(1/binomial(k,n),k);
74 gosper(k/binomial(k,n),k);
75 % gosper(k^10/binomial(k,n),k);
76 gosper(binomial(k-n,k),k);
77 gosper((-1)^k*binomial(n,k),k);
78 gosper((-1)^k/binomial(n,k),k);
92 summand:=binomial(n,k)/2^n$
96 summand:=binomial(n,k)^2/binomial(2*n,n)$
117 % summand:=(-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*binomial(b+c,b+k)*
207 gosper(binomial(a,k),k);
215 gosper(binomial(n,k),k);
222 sumrecursion(binomial(n,k),k,n);
223 sumrecursion(k*binomial(n,k),k,n);
225 % (-1)^k*binomial(2*n,k)*binomial(2*k,k)*binomial(4*n-2*k,2*n-k),k,n);
226 sumrecursion(binomial(n,k)^2,k,n);
227 sumrecursion(binomial(n,k)^2/binomial(2*n,n),k,n);
228 % sumrecursion((-1)^k*binomial(n,k)^2,k,n);
249 % sumrecursion((-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*
250 %    binomial(b+c,b+k)*
252 sumrecursion((-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*
253    binomial(b+c,b+k),k,n);
254 sumrecursion((-1)^(k-n)*binomial(2*n,k)^3,k,n);
256 (-1)^(k-n)*binomial(2*n,k)^3/(binomial(3*n,n)*binomial(2*n,n)),k,n);
272 sumrecursion(binomial(n,k)^2*binomial(n+k,k)^2,k,n);
273 % sumrecursion(4*(-1)^k*binomial(m-1,k)*binomial(2*m-1,2*k)/
274 % binomial(4*m-1,4*k)*(4*m^2+16*k^2-16*k*m+16*k-6*m+3)/
276 sumrecursion((-1)^k*binomial(n,k)*binomial(k,n),k,n);
277 sumrecursion((-1)^k*binomial(n,k)*binomial(2*k,n),k,n);
278 sumrecursion((-1)^k*binomial(n,k)*binomial(k,j)^2,k,n);
279 sumrecursion(binomial(n,k)*binomial(a,k),k,n);
280 sumrecursion((3*k-2*n)*binomial(n,k)^2*binomial(2*k,k),k,n);
281 sumrecursion(binomial(n-k,k),k,n);
282 sumrecursion(binomial(n,k)*binomial(n+k,k),k,n);
283 % sumrecursion(binomial(n+k,m+2*k)*binomial(2*k,k)*(-1)^k/(k+1),k,n);
284 sumrecursion((-1)^k*binomial(n-k,k)*binomial(n-2*k,m-k),k,n);
285 % sumrecursion((-1)^k*binomial(n-k,k)*binomial(n-2*k,m-k),k,m);
286 sumrecursion(binomial(n+k,2*k)*2^(n-k),k,n);
287 sumrecursion(binomial(n,k)*binomial(2*k,k)*(-1/4)^k,k,n);
288 % sumrecursion(binomial(n,i)*binomial(2*n,n-i),i,n);
289 sumrecursion((-1)^k*binomial(n,k)*binomial(2*k,k)*4^(n-k),k,n);
290 sumrecursion((-1)^k*binomial(n,k)/binomial(k+a,k),k,n);
291 % sumrecursion((-1)^k*binomial(n,k)/binomial(k+a,k),k,a);
292 sumrecursion((-1)^(n-k)*binomial(2*n,k)^2,k,n);
299 sumrecursion(binomial(2*n+1,2*p+2*k+1)*binomial(p+k,k),k,n);
300 % sumrecursion(binomial(2*n+1,2*p+2*k+1)*binomial(p+k,k),k,p);
301 sumrecursion(binomial(r,m)*binomial(s,t-m),m,r);
302 % sumrecursion(binomial(r,m)*binomial(s,t-m),m,s);
303 % sumrecursion(binomial(r,m)*binomial(s,t-m),m,t);
304 sumrecursion(binomial(2*n+1,2*k)*binomial(m+k,2*n),k,n);
305 % sumrecursion(binomial(2*n+1,2*k)*binomial(m+k,2*n),k,m);
306 sumrecursion(binomial(n,k)*binomial(k,j)*x^j,k,n);
307 % sumrecursion(binomial(n,k)*binomial(k,j)*x^j,k,j);
308 % sumrecursion(binomial(n,k)*binomial(k,j)*x^k,k,n);
309 sumrecursion(x*binomial(n+k,2*k)*((x^2-1)/4)^(n-k),k,n);
310 sumrecursion(binomial(n+k-1,2*k-1)*(x-1)^(2*k)*x^(n-k)/k,k,n);
312 1/(k+1)*binomial(2*k,k)/(n-k+1)*binomial(2*n-2*k,n-k),k,n);
313 sumrecursion(binomial(m,r)*binomial(n-r,n-r-q)*(t-1)^r,r,m);
314 % sumrecursion(binomial(m,r)*binomial(n-r,n-r-q)*(t-1)^r,r,n);
315 % sumrecursion(binomial(m,r)*binomial(n-r,n-r-q)*(t-1)^r,r,q);
316 % sumrecursion(binomial(m,r)*binomial(n-r,n-r-q)*(t-1)^r,r,r);
324 sumrecursion((-1)^k*binomial(n,k)^3,k,n);
329 % sumrecursion(binomial(n+k+1,n-k)*pochhammer(-n+k,j)*pochhammer(k+1/2,j)*
335 % sumrecursion(binomial(n+k+1,n-k)*pochhammer(-n+k,j)*
392 %    (-1)^n*p^n*binomial(NN,n)*hyperterm({-n,-x},{-NN},1/p,k)$
409 extended_gosper(binomial(k/2,n),k);
410 extended_gosper(binomial(n,k/2)-binomial(n,k/2-1),k);
413 % extended_sumrecursion(binomial(n,k)*binomial(k/2,n),k,n,1,2);
414 sumrecursion(binomial(n,k)*binomial(k/2,n),k,n);
415 extended_sumrecursion(binomial(n/2,k),k,n,2,1);
416 sumrecursion(binomial(n/2,k),k,n);
455 sumtohyper(binomial(n,k)^3,k);
456 sumtohyper(binomial(n,k)/2^n-sub(n=n-1,binomial(n,k)/2^n),k);
457 sumtohyper(binomial(k+j-1,k-j)*2*(-1)^(j+1)*factorial(2*j-1)/
459 % term:=1/(n-1+k)*(1/2-1/2*x)^k/n*binomial(k-n-1,-n-1)*k*
460 %         binomial(n-1+k,n-1);