Rule: Q[1, 60, 62]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{61}-30\cdot t^{59}+\frac{1711}{8}\cdot t^{57}-\frac{3857}{4}\cdot t^{55}+\frac{197505}{64}\cdot t^{53}-\frac{477477}{64}\cdot t^{51}+\frac{28989675}{2048}\cdot t^{49}-\frac{11068785}{512}\cdot t^{47}+\frac{443161355}{16384}\cdot t^{45}-\frac{459884425}{16384}\cdot t^{43}+\frac{6388855935}{262144}\cdot t^{41}-\frac{2334608675}{131072}\cdot t^{39}+\frac{23065933709}{2097152}\cdot t^{37}-\frac{12058015581}{2097152}\cdot t^{35}+\frac{341643774795}{134217728}\cdot t^{33}-\frac{15991836267}{16777216}\cdot t^{31}+\frac{323313211485}{1073741824}\cdot t^{29}-\frac{85794224747}{1073741824}\cdot t^{27}+\frac{304179524103}{17179869184}\cdot t^{25}-\frac{27923456925}{8589934592}\cdot t^{23}+\frac{67282234305}{137438953472}\cdot t^{21}-\frac{8205150525}{137438953472}\cdot t^{19}+\frac{25510558905}{4398046511104}\cdot t^{17}-\frac{483477705}{1099511627776}\cdot t^{15}+\frac{890616825}{35184372088832}\cdot t^{13}-\frac{37550331}{35184372088832}\cdot t^{11}+\frac{17651865}{562949953421312}\cdot t^9-\frac{168113}{281474976710656}\cdot t^7+\frac{29667}{4503599627370496}\cdot t^5-\frac{155}{4503599627370496}\cdot t^3+\frac{31}{576460752303423488}\cdot t$
• $P_3$:
  $2\cdot t^{123}-61\cdot t^{121}+\frac{1815}{2}\cdot t^{119}-\frac{35105}{4}\cdot t^{117}+\frac{7940751}{128}\cdot t^{115}-\frac{87481719}{256}\cdot t^{113}+\frac{390949377}{256}\cdot t^{111}-\frac{2914219715}{512}\cdot t^{109}+\frac{295743055905}{16384}\cdot t^{107}-\frac{1620443352693}{32768}\cdot t^{105}+\frac{7761070794477}{65536}\cdot t^{103}-\frac{32798797170867}{131072}\cdot t^{101}+\frac{3943664897925675}{8388608}\cdot t^{99}-\frac{13257601122548475}{16777216}\cdot t^{97}+\frac{10020680328991185}{8388608}\cdot t^{95}-\frac{27365344140027915}{16777216}\cdot t^{93}+\frac{2167943374648878155}{1073741824}\cdot t^{91}-\frac{4880554216155665775}{2147483648}\cdot t^{89}+\frac{10016902678441083425}{4294967296}\cdot t^{87}-\frac{18783575398520347415}{8589934592}\cdot t^{85}+\frac{515825878251674155935}{274877906944}\cdot t^{83}-\frac{811537431202240939735}{549755813888}\cdot t^{81}+\frac{585869268514986774675}{549755813888}\cdot t^{79}-\frac{777039697070458137225}{1099511627776}\cdot t^{77}+\frac{15157454357521070063469}{35184372088832}\cdot t^{75}-\frac{16994721552372108859041}{70368744177664}\cdot t^{73}+\frac{17528307786355534568901}{140737488355328}\cdot t^{71}-\frac{16631479514735969226315}{281474976710656}\cdot t^{69}+\frac{928986927180251995355595}{36028797018963968}\cdot t^{67}-\frac{745549944100013488831659}{72057594037927936}\cdot t^{65}+\frac{68738647328370037977387}{18014398509481984}\cdot t^{63}-\frac{46564890125670025726617}{36028797018963968}\cdot t^{61}+\frac{1852472802825568414776285}{4611686018427387904}\cdot t^{59}-\frac{1055471517027821364529545}{9223372036854775808}\cdot t^{57}+\frac{550500830449804868558547}{18446744073709551616}\cdot t^{55}-\frac{262437795575589158847333}{36893488147419103232}\cdot t^{53}+\frac{1826461021733140711573863}{1180591620717411303424}\cdot t^{51}-\frac{723435167042483506448175}{2361183241434822606848}\cdot t^{49}+\frac{130165201414008660278925}{2361183241434822606848}\cdot t^{47}-\frac{42446027972411270516295}{4722366482869645213696}\cdot t^{45}+\frac{200102703298510275291105}{151115727451828646838272}\cdot t^{43}-\frac{53098072606098965203605}{302231454903657293676544}\cdot t^{41}+\frac{12642398239547372667525}{604462909807314587353088}\cdot t^{39}-\frac{2689640280075969895675}{1208925819614629174706176}\cdot t^{37}+\frac{16284549332096326822905}{77371252455336267181195264}\cdot t^{35}-\frac{2725543418452127836745}{154742504910672534362390528}\cdot t^{33}+\frac{100270828103589987305}{77371252455336267181195264}\cdot t^{31}-\frac{12883651580041266675}{154742504910672534362390528}\cdot t^{29}+\frac{45883881942953984825}{9903520314283042199192993792}\cdot t^{27}-\frac{4382378928429074469}{19807040628566084398385987584}\cdot t^{25}+\frac{355328021223979011}{39614081257132168796771975168}\cdot t^{23}-\frac{24146653067329221}{79228162514264337593543950336}\cdot t^{21}+\frac{21670073265551865}{2535301200456458802993406410752}\cdot t^{19}-\frac{984741570132705}{5070602400912917605986812821504}\cdot t^{17}+\frac{17714927716673}{5070602400912917605986812821504}\cdot t^{15}-\frac{490136339987}{10141204801825835211973625643008}\cdot t^{13}+\frac{160632918147}{324518553658426726783156020576256}\cdot t^{11}-\frac{2313383215}{649037107316853453566312041152512}\cdot t^9+\frac{21755955}{1298074214633706907132624082305024}\cdot t^7-\frac{119133}{2596148429267413814265248164610048}\cdot t^5+\frac{39711}{664613997892457936451903530140172288}\cdot t^3-\frac{31}{1329227995784915872903807060280344576}\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.