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\pard\li50\ri2\plain\f2\fs22\cf2\protect \par \pard\ri4\plain\f3\fs22\cf0 23. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs22\cf1 {\pntext\f1\'b7\tab}normal(ratn-1-(subs(R,k=k+1)*ratk-R)) \par \pard\li50\ri6\plain\f2\fs22\cf2\protect {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal468 0100090000031701000005001C0000000000050000000B0200000000050000000C023B03340203 0000001E00030000001E00050000000C02D5014001050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 0000000000000000040000002D0101001C000000FB0210FF000000000000900100000001070000 00417269616C00F4774000000022090A4B7DA8F47786A8F4770100000000003000040000002D01 020005000000020101000000050000000102FFFFFF00050000002E011800000005000000090200 00000004000000080100001C000000FB0210FF0000000000009001000000010700000054696D65 73204E657720526F6D616E007DA8F47786A8F4770100000000003000040000002D0103000B0000 0026060F000C004D6174685479706500007B000500000009020000FF0007000000210501003000 3B01640008000000FA0200000000000000000000040000002D01040004000000F0010000070000 00FC020000FFFFFF000000040000002D01000004000000F00101001C000000FB02100007000000 0000BC02000000000102022253797374656D00774000000068090A307DA8F47786A8F477010000 0000003000040000002D010100040000002701FFFF04000000F001020004000000F00103000400 00002701FFFF030000000000 }\plain\f2\fs22\cf2\protect \par \pard\li50\ri2\plain\f2\fs22\cf2\protect \par \pard\ri4\plain\f3\fs22\cf0 24. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs22\cf1 {\pntext\f1\'b7\tab}sum(subs(F,n=0),k=0..0) \par \pard\li50\ri6\plain\f2\fs22\cf2\protect Error: singularity [gamma] \par \pard\li50\ri2\plain\f2\fs22\cf2\protect \par \pard\ri4\plain\f3\fs22\cf0 25./26. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs22\cf1 {\pntext\f1\'b7\tab}PrimDispersion:=proc(q,r,k) \par \pard\li600\ri1\fi-300\plain\f2\fs22\cf1 local s,t,n,a,b,c,d,j; \par begin \par s:=collect(q,k); \par t:=collect(r,k); \par n:=degree(s,k); \par if n=0 or not(n=degree(t,k)) \par then return([]) \par end_if; \par a:=coeff(s,k,n); \par b:=coeff(s,k,n-1); \par c:=coeff(t,k,n); \par d:=coeff(t,k,n-1); \par j:=normal((b*c-a*d)/(a*c*n)); \par if not(testtype(j,DOM_INT) and j>=0) \par then return([]) \par end_if; \par if normal(c*s-a*subs(t,k=k+j))=0 \par then return([j]) \par else return([]) \par end_if; \par end_proc: \par \par DispersionsMenge:=proc(q,r,k) \par local f,g,m,n,i,j,result,tmp,op1,op2; \par begin \par f:=factor(q); \par g:=factor(r); \par m:=(nops(f)-1)/2; \par n:=(nops(g)-1)/2; \par result:=[]; \par for i from 1 to m do \par if m>1 \par then op1:=op(f,2*i) \par else op1:=op(f,2) \par end_if; \par if testtype(op1,"_power") \par then op1:=op(op1,1) \par end_if; \par for j from 1 to n do \par if n>1 \par then op2:=op(g,2*j) \par else op2:=op(g,2) \par end_if; \par if testtype(op2,"_power") \par then op2:=op(op2,1) \par end_if; \par tmp:=PrimDispersion(op1,op2,k); \par if not(tmp=[]) \par then result:=[op(result),tmp[1]] \par end_if; \par end_for; \par end_for; \par \{op(result)\} \par end_proc: \par \par GradSchranke:=proc(A,B,C,k) \par local pol1,pol2,deg1,deg2,a,b; \par begin \par pol1:=collect(A-B,k); \par pol2:=collect(A+B,k); \par if pol1=0 \par then deg1:=-1 \par else deg1:=degree(pol1,k) \par end_if; \par if pol2=0 \par then deg2:=-1 \par else deg2:=degree(pol2,k) \par end_if; \par if deg1<=deg2 \par then return(degree(C,k)-deg2); \par end_if; \par a:=coeff(pol1,k,deg1); \par if deg2=0) \par then return(degree(C,k)-deg1+1); \par else return(max(-2*b/a,degree(C,k)-deg1+1)); \par end_if; \par end_proc: \par \par REtoPol:=proc(A,B,C,k) \par local deg,g,j,rec,sol; \par begin \par deg:=GradSchranke(A,B,C,k); \par if deg<0 \par then return("keine Polynoml\'f6sung") \par end_if; \par g:=_plus(aa[j]*k^j $ j=0..deg); \par rec:=collect(A*subs(g,k=k+1)+B*g-C,k); \par sol:=solve(\{coeff(rec,k,i) $ i=0..degree(rec,k)\},\{aa[j] $ j=0..deg\},IgnoreSpecialCases); \par if sol=NIL or sol=\{\} \par then return("keine Polynoml\'f6sung") \par else subs(g,sol[1]); \par end_if; \par end_proc: \par \par DiskreteStammfunktion:=proc(a,k) \par local u,v,rat,M,dis,g,h,GCD,A,B,CC; \par begin \par rat:=normal(expand(subs(a,k=k+1)/a)); \par u:=numer(rat); \par v:=denom(rat); \par if not(testtype(u,Type::PolyExpr(k)) and \par testtype(v,Type::PolyExpr(k))) \par then return("Eingabe ist kein \par hypergeometrischer Term") \par end_if; \par M:=DispersionsMenge(subs(u,k=k-1),v,k); \par if nops(M)>=1 \par then dis:=max(op(M)); \par else dis:=-1; \par end_if; \par h:=gcd(_mult(subs(u,k=k-1-j) $ j=0..dis), \par _mult(subs(v,k=k+j) $ j=0..dis)); \par if dis=0 \par then A:=normal(u/subs(h,k=k+1)); \par B:=-normal(v/h); \par CC:=v; \par else A:=h*u; \par B:=-subs(h,k=k+1)*v; \par CC:=h*subs(h,k=k+1)*v; \par end_if; \par GCD:=gcd(gcd(A,B),CC); \par A:=normal(A/GCD); \par B:=normal(B/GCD); \par CC:=normal(CC/GCD); \par g:=REtoPol(A,B,CC,k); \par if g="keine Polynoml\'f6sung" \par then return("Eingabe ist nicht \par Gospersummierbar") \par else g/h*a; \par end_if; \par end_proc: \par \par WZCertificate:=proc(F,k,n) \par local a,G; \par begin \par a:=normal(expand(subs(F,n=n+1)-F)); \par G:=DiskreteStammfunktion(a,k); \par factor(normal(expand(G/F))); \par end_proc: \par \pard\ri4\plain\f3\fs22\cf0 27. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs22\cf1 {\pntext\f1\'b7\tab}WZCertificate(binomial(n,k)*x^k*y^(n-k)/(x+y)^n,k,n) \par \pard\li50\ri6\plain\f2\fs22\cf2\protect {\pict\wmetafile8\picw3775\pich1323\picwgoal2140\pichgoal750 010009000003BE0400000C001C0000000000050000000B0200000000050000000C022B05BF0E03 0000001E00030000001E00050000000C02EE025C08050000000B020000000014000000FF060000 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