Testing translation coefficients – found some irregularities.
Former-commit-id: 1f4791f3c6447de48229ccc4eb5a59c6cd7a2968
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Marek Nečada
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4226ed86cd
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6474ceff0b
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@ -312,6 +312,99 @@ Vytvoř náhodně vektor přesunu
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.
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\end_layout
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\begin_layout Enumerate
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TODO
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\end_layout
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\begin_layout Subsection
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Nalezené nesrovnalosti
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\end_layout
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\begin_layout Standard
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Xuovy vzorce ve starší práci
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\begin_inset CommandInset citation
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LatexCommand cite
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after "(77–80)"
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key "xu_calculation_1996"
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\end_inset
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a v novější práci
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\begin_inset CommandInset citation
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LatexCommand cite
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after "(63–65, ...)"
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key "xu_efficient_1998"
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\end_inset
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pro koefficienty
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\begin_inset Formula $B_{mn\mu\nu}$
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\end_inset
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se liší v několika ohledech:
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\end_layout
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\begin_layout Enumerate
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Ve starší práci suma začíná na
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\begin_inset Formula $q=0$
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\end_inset
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, kdežto v novější práci až na
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\begin_inset Formula $q=1$
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\end_inset
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.
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Ovšem členy s
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\begin_inset Formula $q=0$
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\end_inset
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jsou identicky nulové, takže je zbytečné začínat na nule.
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(Ověřeno numericky – i tam jsou to přesně nuly.)
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\end_layout
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\begin_layout Enumerate
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Ve starší práci je poslední člen sumy
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\begin_inset Formula $q=\min\left(n+1,\nu,\frac{n+\nu+1-\left|\mu-m\right|}{2}\right)$
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\end_inset
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, zatímco v novější je to
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\begin_inset Formula $q=\min\left(n,\nu,\frac{n+\nu+1-\left|\mu-m\right|}{2}\right)$
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\end_inset
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.
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Tyto hodnoty se pochopitelně mohou lišit, například pro
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\begin_inset Formula $\left(m,n,\mu,\nu\right)=\left(-1,1,-1,3\right)$
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\end_inset
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.
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Numericky ověřeno, že „přebytečné“ členy ze starší práce jsou nulové (avšak
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vypočtené hodnoty nejsou přesně nuly, něco zbude kvůli zaokrouhlovacích
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chyb).
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\end_layout
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\begin_layout Enumerate
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!!! Některé hodnoty nesedějí, například pro
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\begin_inset Formula $\left(m,n,\mu,\nu\right)=\left(0,1,-1,1\right)$
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\end_inset
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!!!
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\end_layout
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\begin_layout Enumerate
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A nakonec samotné vzorce pro sčítance mají poněkud jiný tvar.
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\end_layout
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\begin_layout Standard
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\begin_inset CommandInset bibtex
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LatexCommand bibtex
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bibfiles "/l/necadam1/repo/qpms/Electrodynamics"
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options "plain"
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\end_inset
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\end_layout
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\end_body
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@ -0,0 +1,46 @@
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#include "translations.h"
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#include "gaunt.h"
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#include <stdio.h>
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//#include <math.h>
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#include <complex.h>
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void qpms_trans_calculator_multipliers_B_general(
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qpms_normalisation_t norm,
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complex double *dest, int m, int n, int mu, int nu, int Qmax) ;
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int lMax=13;
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#define MIN(x,y) ((x)<(y)?(x):(y))
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// Python test: Qmax(M, n, mu, nu) = floor(min(n,nu,(n+nu+1-abs(M+mu))/2))
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// q in IntegerRange(1, Qmax(-m,n,mu,nu))
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int main() {
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qpms_trans_calculator *c = qpms_trans_calculator_init(lMax, QPMS_NORMALISATION_XU);
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complex double dest[lMax + 2];
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for(int n = 1; n <= lMax; ++n)
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for(int nu = 1; nu <= lMax; ++nu)
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for(int m = -n; m <= n; ++m)
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for(int mu = -nu; mu <= nu; ++mu){
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int Qmax = gaunt_q_max(-m, n+1, mu, nu);
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int Qmax_alt = MIN(n,MIN(nu,(n+nu+1-abs(mu-m))));
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qpms_trans_calculator_multipliers_B_general(QPMS_NORMALISATION_XU_CS,
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dest, m, n, mu, nu, Qmax);
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for(int q = 0; q <= Qmax; ++q) {
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// int p = n + nu - 2*q;
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int tubig = cabs(dest[q]) > 1e-8;
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printf("%.16g + %.16g*I, // %d, %d, %d, %d, %d,%s\n",
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creal(dest[q]), cimag(dest[q]), m, n, mu, nu, q,
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q > Qmax_alt ? (tubig?" //tubig":" //tu") : "");
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}
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fflush(stdout);
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}
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qpms_trans_calculator_free(c);
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}
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@ -0,0 +1,26 @@
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(* Vector translation coefficients as in Journal of Computational Physics 139, 137--165 (1998), eqs. (58), (59), (61) *)
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gaunt[m_, n_, mu_, nu_,
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p_] := (-1)^(m + mu) (2 p + 1) Sqrt[
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Factorial[n + m] Factorial[
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nu + mu] Factorial[p - m - mu]/Factorial[n - m]/
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Factorial[nu - mu] / Factorial[p + m + mu]] ThreeJSymbol[{n,
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0}, {nu, 0}, {p, 0}] ThreeJSymbol[{n, m}, {nu,
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mu}, {p, -m - mu}];
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bCXcoeff[m_,n_,mu_,nu_,p_]:=(-1)^(mu+m)(2p+3)Sqrt[(n+m)!(nu+mu)!(p-m-mu+1)!/(n-m)!/(nu-mu)!/(p+m+mu+1)!]ThreeJSymbol[{n,m},{nu,mu},{p+1,-m-mu}]ThreeJSymbol[{n,0},{nu,0},{p,0}]
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p[q_,n_,nu_]:=n+nu-2q;
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ACXcoeff[m_,n_,mu_,nu_,q_]:=(-1)^m (2nu+1)(nu+m)!(nu-mu)!/2/n/(nu+1)/(nu-m)!/(nu+m)!I^p[q,n,nu](n(n+1)+nu(nu+1)-p[q,n,nu](p[q,n,nu]+1))gaunt[-m,n,mu,nu,p[q,n,nu]]
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BCXcoeff[m_,n_,mu_,nu_,q_]:=(-1)^(m+1)(2nu+1)(n+m)!(nu-m)!/2/n/(n+1)/(n-m)!(nu+mu)!I^(p[q,n,nu]+1)Sqrt[((p[q,n,nu]+1)^2-(n-nu)^2)((n+nu+1)^2-(p[q,n,nu]+1)^2)]bCXcoeff[-m,n,mu,nu,p[q,n,nu]]`
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lMax := 5
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For[n = 0, n <= lMax, n++,
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For[nu = 0, nu <= lMax, nu++,
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For[m = -n, m <= n, m++,
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For[mu = -nu, mu <= nu, mu++,
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For[q = 0, q <= Min[n, nu, (n + nu - Abs[m + mu])/2],q++,
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Print[CForm[N[ACXcoeff[m,n,mu,nu,q],16]]]
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]
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]
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]
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]
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]
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@ -0,0 +1,26 @@
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(* Vector translation coefficients as in Journal of Computational Physics 139, 137--165 (1998), eqs. (58), (59), (61) *)
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gaunt[m_, n_, mu_, nu_,
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p_] := (-1)^(m + mu) (2 p + 1) Sqrt[
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Factorial[n + m] Factorial[
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nu + mu] Factorial[p - m - mu]/Factorial[n - m]/
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Factorial[nu - mu] / Factorial[p + m + mu]] ThreeJSymbol[{n,
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0}, {nu, 0}, {p, 0}] ThreeJSymbol[{n, m}, {nu,
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mu}, {p, -m - mu}];
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bCXcoeff[m_,n_,mu_,nu_,p_]:=(-1)^(mu+m)(2p+3)Sqrt[(n+m)!(nu+mu)!(p-m-mu+1)!/(n-m)!/(nu-mu)!/(p+m+mu+1)!]ThreeJSymbol[{n,m},{nu,mu},{p+1,-m-mu}]ThreeJSymbol[{n,0},{nu,0},{p,0}]
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p[q_,n_,nu_]:=n+nu-2q;
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ACXcoeff[m_,n_,mu_,nu_,q_]:=(-1)^m (2nu+1)(nu+m)!(nu-mu)!/2/n/(nu+1)/(nu-m)!/(nu+m)!I^p[q,n,nu](n(n+1)+nu(nu+1)-p[q,n,nu](p[q,n,nu]+1))gaunt[-m,n,mu,nu,p[q,n,nu]]
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BCXcoeff[m_,n_,mu_,nu_,q_]:=(-1)^(m+1)(2nu+1)(n+m)!(nu-m)!/2/n/(n+1)/(n-m)!(nu+mu)!I^(p[q,n,nu]+1)Sqrt[((p[q,n,nu]+1)^2-(n-nu)^2)((n+nu+1)^2-(p[q,n,nu]+1)^2)]bCXcoeff[-m,n,mu,nu,p[q,n,nu]]
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lMax := 18
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For[n = 0, n <= lMax, n++,
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For[nu = 0, nu <= lMax, nu++,
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For[m = -n, m <= n, m++,
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For[mu = -nu, mu <= nu, mu++,
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For[q = 1, q <= Min[n, nu, (n + nu + 1 - Abs[-m + mu])/2],q++,
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Print[CForm[N[BCXcoeff[m,n,mu,nu,q],16]]]
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]
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]
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]
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]
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@ -57,7 +57,7 @@ def printBCXcoeffs(lMax, file=sys.stdout):
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for nu in IntegerRange(lMax+1):
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for m in IntegerRange(-n, n+1):
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for mu in IntegerRange(-nu, nu+1):
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for q in IntegerRange(1, Qmax(-m,n,mu,nu)):
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for q in IntegerRange(1, Qmax(-m,n,mu,nu) +1 ):
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#print(m, n, mu, nu, q, p_q(q,n,nu), file=sys.stderr)
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coeff= BCXcoeff(m, n, mu, nu, q);
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print(N(coeff, prec=53),
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