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## make-win-package bailey baileyLIST NULL bailey-wmprog-maple13-win.txt 13
## Thu Feb  7 15:30:49 EST 2013
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printf("BEGIN bailey package\n");
printf("THIS VERSION DATED Thu Feb  7 15:30:49 EST 2013 \n");
bailey:=table();
bailey[alphadown]:=proc()
  local a,q,alpha,n,x,j:
  requires(qseries):
  if nargs=0 then
    printf("---------------------------------------------------------\n");
    printf("alphadown(a,q,alpha,n)\n");
    printf("   This proc is used to move left in a Bailey chain.\n");
    printf("   In the Bailey chain \n");
    printf("   .. -> (alpha[n]^(-1),beta[n]^(-1)) -> (alpha[n],beta[n]) ->\n");
    printf("   this proc returns alpha[n]^(-1) given alpha.\n");
    printf("   As usual we have assumed rho1,rho2=infinity.\n");
     printf("---------------------------------------------------------\n");
  elif nargs = 4 then
     a:=args[1]:
     q:=args[2]:
     alpha:=args[3]:
     n:=args[4]:
     RETURN(alpha(a,q,n)/a^n/q^(n*n)):
  else
     ERROR(`nargs must be 0 to 4.`);
  fi:
end:
bailey[alphafind]:=proc()
  local x,j,a,q,beta,n;
  requires(qseries):
  if nargs=0 then
    printf("---------------------------------------------------------\n");
    printf("alphafind(a,q,beta,n)\n");
    printf("   This proc is used to find alpha given beta so that \n");
    printf("   (alpha,beta) is a Bailey pair.\n");
    printf("   It returns alpha[n].\n");
    printf("---------------------------------------------------------\n");
  elif nargs = 4 then
     a:=args[1]:
     q:=args[2]:
     beta:=args[3]:
     n:=args[4]:
     x:=0;
     if n=0 then
        RETURN(beta(a,q,0)):
     else
        for j from 0 to n do
           x:=x+aqprod(a*q,q,n+j-1)*(-1)^(n-j)*q^((n-j)*(n-j-1)/2)
                *beta(a,q,j)/aqprod(q,q,n-j);
        od;
        RETURN(simplify(x*(1-a*q^(2*n))));
     fi:
  else
     ERROR(`nargs must be 0 to 4.`);
  fi:
end;
bailey[alphaup]:=proc()
  local a,q,alpha,n:
  requires(qseries):
  if nargs=0 then
    printf("---------------------------------------------------------\n");
    printf("alphaup(a,q,alpha,n)\n");
    printf("   This proc is used to move right in  a Bailey chain.\n");
    printf("   In the Bailey chain \n");
    printf("   .. -> (alpha[n],beta[n]) -> (alpha'[n],beta'[n]) ->\n");
    printf("   this proc returns alpha'[n] given alpha.\n");
    printf("   As usual we have assumed rho1,rho2=infinity.\n");
    printf("---------------------------------------------------------\n");
  elif nargs = 4 then
    a:=args[1]:
    q:=args[2]:
    alpha:=args[3]:
    n:=args[4]:
    RETURN(a^n*q^(n*n)*alpha(a,q,n)):
 fi:
end;
bailey[betadown]:=proc()
  local a,q,beta,n,x,j:
  requires(qseries):
  if nargs=0 then
    printf("---------------------------------------------------------\n");
    printf("betadown(a,q,beta,n)\n");
    printf("   This proc is used to move left in a Bailey chain.\n");
    printf("   In the Bailey chain \n");
    printf("   .. -> (alpha[n]^(-1),beta[n]^(-1)) -> (alpha[n],beta[n]) ->\n");
    printf("   this proc returns beta[n]^(-1) given beta.\n");
    printf("   As usual we have assumed rho1,rho2=infinity.\n");
     printf("---------------------------------------------------------\n");
  elif nargs = 4 then
     a:=args[1]:
     q:=args[2]:
     beta:=args[3]:
     n:=args[4]:
     x:=0:
     for j from 0 to n do
        x:= x + (-1)^(n-j)*a^(-n)*q^(1/2*(n-j-1)*(n-j)-n^2)
                /aqprod(q,q,n-j)*beta(a,q,j):              
     od:
     RETURN(simplify(x)):
  else
     ERROR(`nargs must be 0 to 4.`);
  fi:
end:
bailey[betafind]:=proc()
  local x,j,a,q,alpha,n;
  requires(qseries):
  if nargs=0 then
    printf("---------------------------------------------------------\n");
    printf("betafind(a,q,alpha,n)\n");
    printf("   This proc is used to find beta given alpha so that \n");
    printf("   (alpha,beta) is a Bailey pair.\n");
    printf("   It returns beta[n].\n");
    printf("---------------------------------------------------------\n");
  elif nargs = 4 then
     a:=args[1]:
     q:=args[2]:
     alpha:=args[3]:
     n:=args[4]:
     x:=0;
     for j from 0 to n do
        x:=x+alpha(a,q,j)/aqprod(q,q,n-j)/aqprod(a*q,q,n+j):
     od;
    RETURN(simplify(x));
  fi:
end;
bailey[betaup]:=proc()
  local a,q,beta,n,x,j:
  requires(qseries):
  if nargs=0 then
    printf("---------------------------------------------------------\n");
    printf("betaup(a,q,beta,n)\n");
    printf("   This proc is used to move right in  a Bailey chain.\n");
    printf("   In the Bailey chain \n");
    printf("   .. -> (alpha[n],beta[n]) -> (alpha'[n],beta'[n]) ->\n");
    printf("   this proc returns beta'[n] given beta.\n");
    printf("   As usual we have assumed rho1,rho2=infinity.\n");
    printf("---------------------------------------------------------\n");
  elif nargs = 4 then
    a:=args[1]:
    q:=args[2]:
    beta:=args[3]:
    n:=args[4]:
    x:=0;
    for j from 0 to n do
        x:=x+a^j*q^(j*j)*beta(a,q,j)/aqprod(q,q,n-j);
    od;
    RETURN(x):
 fi:
end;
printf("TABLE TYPE bailey = %a\n",type(bailey,table));
save( bailey 
,
"c:\\Program Files\\Maple 13\\mylib\\bailey.m");
printf("END bailey package\n");
## mylib  above must be changed to the name of the directory
## in which you want stuff stored