Chebyshev Series Rationals¶
Equations 1401-1410: Chebyshev Series Rationals¶
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'))¶
1401 z=(a+dT1(x')+eT1(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y'))
1402 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y'))
1403 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y'))
1404 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y'))
1405 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y'))
1406 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y'))
1407 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y'))
1408 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y'))
1409 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y')+
anT9(x')+aoT9(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y')+apT10(x')+aqT10(y'))
1410 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y')+
anT9(x')+aoT9(y')+arT10(x')+asT10(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y')+apT10(x')+aqT10(y')+atT11(x')+auT11(y'))
Equations 1421-1430: Chebyshev Series LnX Rationals¶
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'))¶
1421 z=(a+dT1(x')+eT1(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y'))
1422 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y'))
1423 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y'))
1424 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y'))
1425 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y'))
1426 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y'))
1427 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y'))
1428 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y'))
1429 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y')+
anT9(x')+aoT9(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y')+apT10(x')+aqT10(y'))
1430 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y')+
anT9(x')+aoT9(y')+arT10(x')+asT10(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y')+apT10(x')+aqT10(y')+atT11(x')+auT11(y'))
Equations 1441-1450: Chebyshev Series LnY Rationals¶
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'))¶
1441 z=(a+dT1(x')+eT1(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y'))
1442 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y'))
1443 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y'))
1444 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y'))
1445 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y'))
1446 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y'))
1447 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y'))
1448 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y'))
1449 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y')+
anT9(x')+aoT9(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y')+apT10(x')+aqT10(y'))
1450 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y')+
anT9(x')+aoT9(y')+arT10(x')+asT10(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y')+apT10(x')+aqT10(y')+atT11(x')+auT11(y'))
Equations 1461-1470: Chebyshev Series LnX,LnY Rationals¶
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'))¶
1461 z=(a+dT1(x')+eT1(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y'))
1462 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y'))
1463 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y'))
1464 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y'))
1465 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y'))
1466 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y'))
1467 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y'))
1468 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y'))
1469 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y')+
anT9(x')+aoT9(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y')+apT10(x')+aqT10(y'))
1470 z=(a+dT1(x')+eT1(y')+hT2(x')+iT2(y')+lT3(x')+mT3(y')+pT4(x')+qT4(y')+
tT5(x')+uT5(y')+abT6(x')+acT6(y')+afT7(x')+agT7(y')+ajT8(x')+akT8(y')+
anT9(x')+aoT9(y')+arT10(x')+asT10(y'))/
(1+bT1(x')+cT1(y')+fT2(x')+gT2(y')+jT3(x')+kT3(y')+nT4(x')+oT4(y')+
rT5(x')+sT5(y')+vT6(x')+aaT6(y')+adT7(x')+aeT7(y')+ahT8(x')+aiT8(y')+
alT9(x')+amT9(y')+apT10(x')+aqT10(y')+atT11(x')+auT11(y'))