Rule: Q[4, 60, 65]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{64}-252\cdot t^{62}+1891\cdot t^{60}-\frac{17995}{2}\cdot t^{58}+\frac{487635}{16}\cdot t^{56}-\frac{2503193}{32}\cdot t^{54}+\frac{20237679}{128}\cdot t^{52}-\frac{66096459}{256}\cdot t^{50}+\frac{1420494075}{4096}\cdot t^{48}-\frac{3179201025}{8192}\cdot t^{46}+\frac{11965356585}{32768}\cdot t^{44}-\frac{19055938265}{65536}\cdot t^{42}+\frac{103189703435}{524288}\cdot t^{40}-\frac{119065042425}{1048576}\cdot t^{38}+\frac{234461414075}{4194304}\cdot t^{36}-\frac{196947587823}{8388608}\cdot t^{34}+\frac{2254848913647}{268435456}\cdot t^{32}-\frac{1370594437707}{536870912}\cdot t^{30}+\frac{1409476549415}{2147483648}\cdot t^{28}-\frac{609590544255}{4294967296}\cdot t^{26}+\frac{880519675035}{34359738368}\cdot t^{24}-\frac{263012370465}{68719476736}\cdot t^{22}+\frac{128447901855}{274877906944}\cdot t^{20}-\frac{25264080075}{549755813888}\cdot t^{18}+\frac{31426050825}{8796093022208}\cdot t^{16}-\frac{3771126099}{17592186044416}\cdot t^{14}+\frac{676868787}{70368744177664}\cdot t^{12}-\frac{43541267}{140737488355328}\cdot t^{10}+\frac{7565085}{1125899906842624}\cdot t^8-\frac{202895}{2251799813685248}\cdot t^6+\frac{5797}{9007199254740992}\cdot t^4-\frac{33}{18014398509481984}\cdot t^2+\frac{1}{1152921504606846976}$
• $P_3$:
  $16\cdot t^{129}-512\cdot t^{127}+8001\cdot t^{125}-81375\cdot t^{123}+\frac{9691375}{16}\cdot t^{121}-\frac{28143753}{8}\cdot t^{119}+\frac{2124702041}{128}\cdot t^{117}-\frac{8372954733}{128}\cdot t^{115}+\frac{899749479915}{4096}\cdot t^{113}-\frac{653537041885}{1024}\cdot t^{111}+\frac{53197915209439}{32768}\cdot t^{109}-\frac{119603868954453}{32768}\cdot t^{107}+\frac{3832053903054819}{524288}\cdot t^{105}-\frac{3439022733510735}{262144}\cdot t^{103}+\frac{88991066104097985}{4194304}\cdot t^{101}-\frac{130262285166868065}{4194304}\cdot t^{99}+\frac{11086006058675034795}{268435456}\cdot t^{97}-\frac{1679348132782110945}{33554432}\cdot t^{95}+\frac{119020466870986116975}{2147483648}\cdot t^{93}-\frac{120713503384086915225}{2147483648}\cdot t^{91}+\frac{1797533804937585155805}{34359738368}\cdot t^{89}-\frac{768801046323239784855}{17179869184}\cdot t^{87}+\frac{9683786916818990017315}{274877906944}\cdot t^{85}-\frac{7023795061569239000775}{274877906944}\cdot t^{83}+\frac{150326884242264907670675}{8796093022208}\cdot t^{81}-\frac{23193290711663728612047}{2199023255552}\cdot t^{79}+\frac{422831530666484898542703}{70368744177664}\cdot t^{77}-\frac{222438881468920318794669}{70368744177664}\cdot t^{75}+\frac{1729041725703792393992175}{1125899906842624}\cdot t^{73}-\frac{387838994123383954541775}{562949953421312}\cdot t^{71}+\frac{2570079734390957672096829}{9007199254740992}\cdot t^{69}-\frac{982308090075136314555093}{9007199254740992}\cdot t^{67}+\frac{44324146676655640642475727}{1152921504606846976}\cdot t^{65}-\frac{900052962818686860906255}{72057594037927936}\cdot t^{63}+\frac{34466734046762655673527765}{9223372036854775808}\cdot t^{61}-\frac{9484830572267016523692603}{9223372036854775808}\cdot t^{59}+\frac{38365354867964220501271971}{147573952589676412928}\cdot t^{57}-\frac{4448641846067342045919069}{73786976294838206464}\cdot t^{55}+\frac{15117238309862706952379445}{1180591620717411303424}\cdot t^{53}-\frac{2934848463086899151927145}{1180591620717411303424}\cdot t^{51}+\frac{16630807957492428527587155}{37778931862957161709568}\cdot t^{49}-\frac{669972258084786789135465}{9444732965739290427392}\cdot t^{47}+\frac{3135238142812357225348215}{302231454903657293676544}\cdot t^{45}-\frac{414847067813984717066925}{302231454903657293676544}\cdot t^{43}+\frac{791980765826698096218675}{4835703278458516698824704}\cdot t^{41}-\frac{42446027972411270516295}{2417851639229258349412352}\cdot t^{39}+\frac{65119061547736545450465}{38685626227668133590597632}\cdot t^{37}-\frac{5558740706330753559345}{38685626227668133590597632}\cdot t^{35}+\frac{26889843254201612746425}{2475880078570760549798248448}\cdot t^{33}-\frac{223573904607874331225}{309485009821345068724781056}\cdot t^{31}+\frac{831694925141292512157}{19807040628566084398385987584}\cdot t^{29}-\frac{41904708315632261099}{19807040628566084398385987584}\cdot t^{27}+\frac{29010951910822334607}{316912650057057350374175801344}\cdot t^{25}-\frac{533158880987913525}{158456325028528675187087900672}\cdot t^{23}+\frac{262941904268893025}{2535301200456458802993406410752}\cdot t^{21}-\frac{6693066654117277}{2535301200456458802993406410752}\cdot t^{19}+\frac{4418974509089013}{81129638414606681695789005144064}\cdot t^{17}-\frac{18053969395461}{20282409603651670423947251286016}\cdot t^{15}+\frac{7263091136105}{649037107316853453566312041152512}\cdot t^{13}-\frac{67620089355}{649037107316853453566312041152512}\cdot t^{11}+\frac{7084009361}{10384593717069655257060992658440192}\cdot t^9-\frac{15147561}{5192296858534827628530496329220096}\cdot t^7+\frac{603603}{83076749736557242056487941267521536}\cdot t^5-\frac{715}{83076749736557242056487941267521536}\cdot t^3+\frac{65}{21267647932558653966460912964485513216}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.