SetDirectory["c:/diskE/job2008/Zurich"];

<<pslq.m

(*  a onefold MB integral from the calculation of 
the double box   *)

MBint[(1/6) (π^2) ((Gamma[-z3])^2) Gamma[z3] Gamma[1+z3]-((Gamma[-z3])^2) Gamma[z3] Gamma[1+z3] PolyGamma[1,1+z3],{{ep->0},{z3->-(3/8)}}];

num=NIntegrate[%[[1]]/(2Pi)  /.{z3->-(3/8)+I*y1},{y1,-Infinity,Infinity} ,Method->DoubleExponential,WorkingPrecision->100]

%/Zeta[4]

(4+1/4)Zeta[4]

%-num

(1/6) (π^2) ((Gamma[-z3])^2) Gamma[z3] Gamma[1+z3]-((Gamma[-z3])^2) Gamma[z3] Gamma[1+z3] (PolyGamma[1,1+z3]+1);

num=NIntegrate[%/(2Pi)  /.{z3->-(3/8)+I*y1},{y1,-Infinity,Infinity} ,Method->DoubleExponential,WorkingPrecision->100]

x0=  6.2448078101205637504154308769459887760116414468613877953882071450075200891978184717004948533719833535432302176506999`100.15051499783199;
x[1]=N[Zeta[4],200] ;
x[2]=N[ Zeta[3],200] ;
x[3]=N[ Zeta[2],200] ;
x[4]=N[ 1,200] ;

PSLQ[{x[1],x[2],x[3],x[4], x0},50]

PSLQ[{x[1],x[2],x[3],x[4], x0},100]

%/4

(17/4)Zeta[4]+Zeta[2]

%-x0

(*   For example, this is the list of constants up to level 6 where Log[2] is involved   *)

x[1]=N[Zeta[5],500] ;  
x[2]=N[ Zeta[3]Zeta[2],500] ; 
x[3]=N[ Log[2]Zeta[4],500] ;   
x[4]=N[PolyLog[5,1/2],500] ;
x[5]=N[Log[2]PolyLog[4,1/2],500] ;
x[6]=N[Log[2]^5,500] ;
x[7]=N[ Log[2]^2Zeta[3],500] ; 
x[8]=N[ Log[2]^3Zeta[2],500] ;  
x[9]=N[ Zeta[4],500] ;   
x[10]=N[PolyLog[4,1/2],500] ;
x[11]=N[Log[2]^4,500] ;
x[12]=N[ Log[2]^2Zeta[2],500] ;   
x[13]=N[ Zeta[3]Log[2],500] ;   
x[14]=N[ Zeta[3],500] ;  
x[15]=N[ Log[2]Zeta[2],500] ;   
x[16]=N[Log[2]^3,500] ;
x[17]=N[Zeta[2],500] ;   
x[18]=N[Log[2]^2,500] ;
x[19]=N[Log[2],500] ;
x[20]=N[Zeta[6],500] ;   
x[21]=N[Zeta[5]Log[2],500] ; 
x[22]=N[Zeta[4]Log[2]^2,500] ;  
x[23]=N[Zeta[3]Log[2]^3,500] ;  
x[24]=N[Zeta[3]^2,500] ;   
x[25]=N[Zeta[3]Zeta[2]Log[2],500] ;  
x[26]=N[Log[2]^6,500] ;
x[27]=N[Zeta[2]Log[2]^4,500] ;   
x[28]=N[PolyLog[6,1/2],500] ;
x[29]=N[PolyLog[5,1/2]Log[2],500] ;
x[30]=N[PolyLog[4,1/2]Log[2]^2,500] ;
x[31]=N[PolyLog[4,1/2]Zeta[2],500] ;
x[32]=N[1,500] ;
x[33]=N[appHPLs6,500] ;

appHPLs6=0.98744142640329971377165000804182021413602714891426845727515905154561369911878895355863956404477558915203056255385484634405674146808430963398029349014388073675782238914431072868245446242746979584265585272725425183010859167628333328685038039329144638374255888866551887721158448693857022393231698312530376047305702516583202905810931661490473936355942820783847449825120107884979332566716367272547925735281416166238736093320673713594250387141809300098954218750377349286950447367387499265350018206576197727;