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Member "pari-2.13.1/src/test/in/hypergeom" (14 Jan 2021, 4034 Bytes) of package /linux/misc/pari-2.13.1.tar.gz:

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    1 default(realprecision,38);
    2 testF(v, D0, D) =
    3 {
    4   for(i=1,#v,
    5     my ([n,d,z] = v[i]);
    6     localbitprec(D);
    7     a = hypergeom(n,d,z);
    8     localbitprec(D + 64);
    9     b = hypergeom(n,d,z);
   10     e = exponent(a/b - 1);
   11     if (e > -D0, print(i,": ", e));
   12   );
   13 }
   14 { localbitprec(320);
   15 v11=[
   16 [0.1,0.2,0.5], [-0.1,0.2,0.5], [0.1,0.2,-0.5+I], [1+I,1+I,1-I],
   17 /*5*/
   18 [10^(-8),10^(-8),10^(-10)], [10^(-8),10^(-12),-10^(-10)+10^(-12)*I], [1,1,10+10^(-9)*I], [1,3,10], [500,511,10],
   19 /*10*/
   20 [8.1,10.1,100], [1,2,600], [100,1.5,2.5], [-60,1,10], [60,1,10],
   21 /*15*/
   22 [60,1,-10], [-60,1,-10], [1000,1,10^(-3)], [10^(-3),1,700], [500,1,-5],
   23 /*20*/
   24 [-500,1,5], [20,-10+10^(-9),-2.5], [20,10-10^(-9),2.5], [-20,-10+10^(-12),2.5], [50,10,200*I],
   25 /*25*/
   26 [-5,(-5+10^(-9))*(1+I),-1], [4,80,200], [-4,500,300], [5,0.1,-2+300*I], [-5,0.1,2+300*I],
   27 /*30*/
   28 [2+8*I,-150+I,150], [5,2,100-1000*I], [-5,2,-100+1000*I], [-5,-2-I,1+(2-10^(-10))*I], [1,10^(-12),1],
   29 /*35*/
   30 [10,10^(-12),10], [1,-1+10^(-12)*I,1], [1000,1,-1000], [-1000,1,1000], [-10+500*I,5*I,10],
   31 /*40*/
   32 [20,10+1000*I,-5]];
   33 }
   34 print("1F1");
   35 testF(v11, 128, 128)
   36 testF(v11, 256, 256)
   37 
   38 hypergeom([],[],-3.5)
   39 hypergeom(1.5,[],0.5)
   40 hypergeom(-0.5,[],3)
   41 hypergeom([],2.5,15)
   42 hypergeom([],2.5,-15)
   43 hypergeom([],2.5,15*I)
   44 v20=[[[1,1],[],-3], [[1,1],[],-3+10^-20*I], [[1,3/2],[],-3], [[1,-1],[],10^-4]];
   45 print("2F0");
   46 testF(v20, 128, 128)
   47 
   48 {localbitprec(320);
   49 v21=[
   50 [[0.1,0.2],0.3,0.5],
   51 [[-0.1,0.2],0.3,0.5],
   52 [[0.1,0.2],-0.3,-0.5+0.5*I],
   53 [[10^(-8),10^(-8)],10^(-8),10^(-6)],
   54 [[10^(-8),-10^(-6)],10^(-12),-10^(-10)+10^(-12)*I],
   55 [[1,10],1,0.5+10^(-9)*I],
   56 [[1,-1+10^(-12)*I],1,-0.8],
   57 [[2+8*I,3-5*I],sqrt(2)-Pi*I,0.75],
   58 [[100,200],350,I],
   59 /*10*/
   60 [[2+10^(-9),3],5,-0.75],
   61 [[-2,-3],-5+10^(-9),0.5],
   62 [[-1,-1.5],-2-10^(-15),0.5],
   63 [[500,-500],500,0.75],
   64 [[500,500],500,-0.6],
   65 [[-1000,-2000],-4000.1,-0.5],
   66 [[-100,-200],-300+10^(-9),0.5*sqrt(2)],
   67 [[300,10],5,0.5],
   68 [[5,-300],10,0.5],
   69 [[10,5],-300.5,0.5],
   70 /*20*/
   71 [[2+200*I,5],10,0.6],
   72 [[2+200*I,5-100*I],10+500*I,0.8],
   73 [[2,5],10-500*I,-0.8],
   74 [[2.25,3.75],-0.5,-1],
   75 [[1,2],4+3*I,0.6-0.8*I],
   76 [[1,0.9],2,exp(I*Pi/3)],
   77 [[1,2.5],5,exp(I*Pi/3)],
   78 [[-1,0.9],2,exp(-I*Pi/3)],
   79 [[4,1.1],2,0.5+(0.5*sqrt(3)-0.01)*I],
   80 [[5,2.2],-2.5,0.49+0.5*sqrt(3)*I],
   81 /*30*/
   82 [[2/3,1],4/3,exp(I*Pi/3)],
   83 [[1/2,5/2],5,3/4],
   84 [[1/2,1/5],3,3/5+9/10*I],
   85 [[1/2,1/5],3,3/5+I],
   86 [[-2,-4/5],-9/5,3/5],
   87 [[1,2],4,1],
   88 [[-1/2,-3/2],4,99/100],
   89 [[10,-1],2,1+I],
   90 [[1,-10],2,1+2*I],
   91 [[-2,1/2],1,100],
   92 /*40*/
   93 [[-2,1/2],1,-100],
   94 [[3/2,3/2],1,0.97],
   95 [[3/2,3/2],1,1.03],
   96 [[3/2,-1/2],4/3,exp(I*Pi/3)],
   97 [[1/2,1/3],11/6, 101/100 + I/2^30]
   98 ];
   99 }
  100 print("2F1");
  101 testF(v21, 125, 128)
  102 testF(v21, 250, 256)
  103 
  104 v31=[[[1,1,2],[3],-3], [[1,1,2],[3],-3+10^-20*I], [[1,3/2,2],[3],-3], [[1,-1,2],[3],10^-4]];
  105 print("3F1");
  106 testF(v31, 128, 128)
  107 
  108 v32=[[[1,1,2],[3,I],-3], [[1,1,2],[3,I],-3+10^-20*I], [[1,3/2,2],[3,I],-3], [[1,-1,2],[3,I],10^-4]];
  109 print("3F2");
  110 testF(v32, 128, 128)
  111 
  112 localprec(115); hyperu(5/6,5/3,230) \\ cancellation in F11
  113 
  114 hypergeom([1,1],2,-1.000000000000001)
  115 f(a,c)=exponent( hypergeom([a,2],c,(c-2)/(a-1)) - (a-1)*(c-1)/(a+1-c) );
  116 for(j=28,32,print(j/5,": ",f(3,j/5)));
  117 f(4,1/5)
  118 hypergeom([3,2],3.4,0.7)
  119 hypergeom([1.5,2.1],[-3.5,1.1],1)
  120 a=sqrt(Pi)*(1-erfc(sqrt(2)))/sqrt(2)+exp(-2)/2-1/2;
  121 b=hypergeom([1/2,1],[3/2,2],-2); exponent(a-b)
  122 a=5/3;
  123 T1=hypergeom([1,1,1],[a,a],1);
  124 hypergeom([1,1,1],[a,a],-1)
  125 T2=hypergeom([2,1,1],[a+1,a+1],1)
  126 T3=hypergeom([2*a-1,1,1],[a+1,a+1],1)
  127 b=T1+(a-1)^2/(a^2*(2*a-3))*(T2-2*(a-1)*T3)-gamma(a)^2/((2*a-3)*gamma(2*a-2));
  128 exponent(b) <= -122
  129 airy(0)
  130 airy(I)
  131 airy(1)
  132 airy(100)[1]
  133 airy(-100)[2]
  134 hypergeom([1,1,1,1/2],[3/4,3/2,3/2],1)
  135 hypergeom([1,2,1,1,1,1/2],[1,2,3/4,3/2,3/2],1)
  136 F(k,a)=Pi^(k-1/2)*gamma(a)/(2^(3*k-1)*gamma(a+1/2))*hypergeom(concat(vector(k,j,1),1/2),concat(a+1/2,vector(k-1,j,3/2)),1);
  137 L=lfuninit(lfunetaquo([4,2;8,2]),[1,6,1],2);
  138 lindep([lfun(L,3),F(3,5/4),F(3,3/4),F(3,1/4)])
  139 
  140 hypergeom([1/6,2/3],1/2,2)
  141 
  142 \\ Errors, keep at end
  143 airy(O(x))
  144 hypergeom([],[],O(x))
  145 hypergeom([2,1],0,1)
  146 hypergeom([2,3],1,1)
  147 hypergeom([1/2,1/2,1/2],[1/3,1/3], 1 - 10^-6)
  148 hypergeom([1,2,3,4],[],1/2)