Chebyshev Series Polynomials¶
Equations 401-409: Chebyshev Series X,Y Bivariate Polynomials¶
x' is x scaled -1 to +1 y' is y scaled -1 to +1 Tn(x') = cos(n*acos(x')) Tn(y') = cos(n*acos(y'))¶
401 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')
402 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')
403 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')
404 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')
405 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')
406 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')
407 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')
408 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')+
bbT9(x')+bcT8(x')T1(y')+bdT7(x')T2(y')+beT6(x')T3(y')+bfT5(x')T4(y')+bgT4(x')T5(y')+bhT3(x')T6(y')+biT2(x')T7(y')+
bjT1(x')T8(y')+bkT9(y')
409 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')+
bbT9(x')+bcT8(x')T1(y')+bdT7(x')T2(y')+beT6(x')T3(y')+bfT5(x')T4(y')+bgT4(x')T5(y')+bhT3(x')T6(y')+biT2(x')T7(y')+
bjT1(x')T8(y')+bkT9(y')+
blT10(x')+bmT9(x')T1(y')+bnT8(x')T2(y')+boT7(x')T3(y')+bpT6(x')T4(y')+bqT5(x')T5(y')+brT4(x')T6(y')+bsT3(x')T7(y')+
btT2(x')T8(y')+buT1(x')T9(y')+bvT10(y')
Equations 421-429: Chebyshev Series LnX,Y Bivariate Polynomials¶
x' is ln(x) scaled -1 to +1 y' is y scaled -1 to +1 Tn(x') = cos(n*acos(x')) Tn(y') = cos(n*acos(y'))¶
421 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')
422 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')
423 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')
424 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')
425 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')
426 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')
427 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')
428 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')+
bbT9(x')+bcT8(x')T1(y')+bdT7(x')T2(y')+beT6(x')T3(y')+bfT5(x')T4(y')+bgT4(x')T5(y')+bhT3(x')T6(y')+biT2(x')T7(y')+
bjT1(x')T8(y')+bkT9(y')
429 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')+
bbT9(x')+bcT8(x')T1(y')+bdT7(x')T2(y')+beT6(x')T3(y')+bfT5(x')T4(y')+bgT4(x')T5(y')+bhT3(x')T6(y')+biT2(x')T7(y')+
bjT1(x')T8(y')+bkT9(y')+
blT10(x')+bmT9(x')T1(y')+bnT8(x')T2(y')+boT7(x')T3(y')+bpT6(x')T4(y')+bqT5(x')T5(y')+brT4(x')T6(y')+bsT3(x')T7(y')+
btT2(x')T8(y')+buT1(x')T9(y')+bvT10(y')
Equations 441-449: Chebyshev Series X,LnY Bivariate Polynomials¶
x' is x scaled -1 to +1 y' is ln(y) scaled -1 to +1 Tn(x') = cos(n*acos(x')) Tn(y') = cos(n*acos(y'))¶
441 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')
442 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')
443 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')
444 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')
445 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')
446 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')
447 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')
448 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')+
bbT9(x')+bcT8(x')T1(y')+bdT7(x')T2(y')+beT6(x')T3(y')+bfT5(x')T4(y')+bgT4(x')T5(y')+bhT3(x')T6(y')+biT2(x')T7(y')+
bjT1(x')T8(y')+bkT9(y')
449 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')+
bbT9(x')+bcT8(x')T1(y')+bdT7(x')T2(y')+beT6(x')T3(y')+bfT5(x')T4(y')+bgT4(x')T5(y')+bhT3(x')T6(y')+biT2(x')T7(y')+
bjT1(x')T8(y')+bkT9(y')+
blT10(x')+bmT9(x')T1(y')+bnT8(x')T2(y')+boT7(x')T3(y')+bpT6(x')T4(y')+bqT5(x')T5(y')+brT4(x')T6(y')+bsT3(x')T7(y')+
btT2(x')T8(y')+buT1(x')T9(y')+bvT10(y')
Equations 461-469: Chebyshev Series LnX,LnY Bivariate Polynomials¶
x' is ln(x) scaled -1 to +1 y' is ln(y) scaled -1 to +1 Tn(x') = cos(n*acos(x')) Tn(y') = cos(n*acos(y'))¶
461 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')
462 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')
463 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')
464 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')
465 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')
466 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')
467 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')
468 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')+
bbT9(x')+bcT8(x')T1(y')+bdT7(x')T2(y')+beT6(x')T3(y')+bfT5(x')T4(y')+bgT4(x')T5(y')+bhT3(x')T6(y')+biT2(x')T7(y')+
bjT1(x')T8(y')+bkT9(y')
469 z=a+bT1(x')+cT1(y')+dT2(x')+eT1(x')T1(y')+fT2(y')+gT3(x')+hT2(x')T1(y')+iT1(x')T2(y')+jT3(y')+
kT4(x')+lT3(x')T1(y')+mT2(x')T2(y')+nT1(x')T3(y')+oT4(y')+
pT5(x')+qT4(x')T1(y')+rT3(x')T2(y')+sT2(x')T3(y')+tT1(x')T4(y')+uT5(y')+
vT6(x')+aaT5(x')T1(y')+abT4(x')T2(y')+acT3(x')T3(y')+adT2(x')T4(y')+aeT1(x')+T5(y')+afT6(y')+
agT7(x')+ahT6(x')T1(y')+aiT5(x')T2(y')+ajT4(x')T3(y')+akT3(x')T4(y')+alT2(x')T5(y')+amT1(x')T6(y')+anT7(y')+
aoT8(x')+apT7(x')T1(y')+aqT6(x')T2(y')+arT5(x')T3(y')+asT4(x')T4(y')+atT3(x')T5(y')+auT2(x')T6(y')+avT1(x')T7(y')+baT8(y')+
bbT9(x')+bcT8(x')T1(y')+bdT7(x')T2(y')+beT6(x')T3(y')+bfT5(x')T4(y')+bgT4(x')T5(y')+bhT3(x')T6(y')+biT2(x')T7(y')+
bjT1(x')T8(y')+bkT9(y')+
blT10(x')+bmT9(x')T1(y')+bnT8(x')T2(y')+boT7(x')T3(y')+bpT6(x')T4(y')+bqT5(x')T5(y')+brT4(x')T6(y')+bsT3(x')T7(y')+
btT2(x')T8(y')+buT1(x')T9(y')+bvT10(y')