In[]:=
$Version
Out[]=
14.2.0 for Microsoft Windows (64-bit) (December 26, 2024)
(*-Example1:---------------------------------------------------------------------------------------------------*)
In[]:=
F[z_]:=FoxH[{{{1/2,2},{2,2}},{{1,2}}},{{{1,2}},{{1,2}}},z]//N;
In[]:=
G[z_?NumericQ]:=1/(2PiI)NContourIntegrateGamma[-4s]Gamma[2s+1]Sin[2πs]*z^-s,s∈InfiniteLine[{-1,0},{0,1}];
1+4s
2
π
(1+2s)In[]:=
Table[{F[z],G[z]},{z,1/2,5,1/4}]//Chop//MatrixForm
Out[]//MatrixForm=
0.131235 | 0.131235 |
0.195988 | 0.195988 |
0.253641 | 0.253641 |
0.305852 | 0.305852 |
0.353804 | 0.353804 |
0.398333 | 0.398333 |
0.440043 | 0.440043 |
0.479382 | 0.479382 |
0.516697 | 0.516697 |
0.552258 | 0.552258 |
0.58628 | 0.58628 |
0.618941 | 0.618941 |
0.650385 | 0.650385 |
0.680734 | 0.680734 |
0.710091 | 0.710091 |
0.738544 | 0.738544 |
0.76617 | 0.76617 |
0.793033 | 0.793033 |
0.819192 | 0.819192 |
In[]:=
Plot[Sin[z]-z^2+F[z]==0,{z,0,2}]
Out[]=
In[]:=
FindRoot[Sin[z]-z^2+F[z]==0,{z,1}]
Out[]=
{z1.07073}
In[]:=
FindRoot[Sin[z]-z^2+G[z]==0,{z,1}]//Quiet
Out[]=
{z1.07073+0.}
(*-Example2:---------------------------------------------------------------------------------------------------*)
In[]:=
G2[z_?NumericQ]:=1/(2PiI)NContourIntegrate*z^-s,s∈InfiniteLine[{-1/5,0},{0,1}];
1+4s
2
π
Gamma[-4s]Gamma[z+2s]Gamma[1-z-2s]Gamma[1+2s]
In[]:=
Plot[z-FoxH[{{{1/2,2},{1,2}},{{1,2}}},{{{z,2}},{{z,2}}},z],{z,0,1}]
Out[]=
In[]:=
FindRoot[z-FoxH[{{{1/2,2},{1,2}},{{1,2}}},{{{z,2}},{{z,2}}},z]==0,{z,1/2}]
Out[]=
{z0.497491}
In[]:=
FindRoot[z-G2[z]==0,{z,1/2}]//Chop
Out[]=
{z0.497491}