Rule: Q[28, 29, 58]

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.

• $P_1$:
  $268435456\cdot t^{28}-1811939328\cdot t^{26}+5452595200\cdot t^{24}-9646899200\cdot t^{22}+11142168576\cdot t^{20}-8820883456\cdot t^{18}+4889837568\cdot t^{16}-1905131520\cdot t^{14}+515973120\cdot t^{12}-94595072\cdot t^{10}+11202048\cdot t^8-792064\cdot t^6+29120\cdot t^4-420\cdot t^2+1$
• $P_2$:
  $268435456\cdot t^{57}-3758096384\cdot t^{55}+24914165760\cdot t^{53}-104035516416\cdot t^{51}+307049267200\cdot t^{49}-681301770240\cdot t^{47}+1180267970560\cdot t^{45}-1636506009600\cdot t^{43}+1847206158336\cdot t^{41}-1717357199360\cdot t^{39}+1325585088256\cdot t^{37}-853810124544\cdot t^{35}+460160347920\cdot t^{33}-207662105728\cdot t^{31}+78378960360\cdot t^{29}-24668106904\cdot t^{27}+\frac{51538723353}{8}\cdot t^{25}-\frac{5545773675}{4}\cdot t^{23}+\frac{31179571995}{128}\cdot t^{21}-\frac{4418157975}{128}\cdot t^{19}+\frac{7952684355}{2048}\cdot t^{17}-\frac{173996955}{512}\cdot t^{15}+\frac{184542225}{8192}\cdot t^{13}-\frac{8940555}{8192}\cdot t^{11}+\frac{9641775}{262144}\cdot t^9-\frac{105183}{131072}\cdot t^7+\frac{169911}{16777216}\cdot t^5-\frac{1015}{16777216}\cdot t^3+\frac{29}{268435456}\cdot t$
• $P_3$:
  $268435456\cdot t^{115}-7650410496\cdot t^{113}+106166222848\cdot t^{111}-955965767680\cdot t^{109}+6279926906880\cdot t^{107}-32084203143168\cdot t^{105}+132711931183104\cdot t^{103}-456838646464512\cdot t^{101}+1335089794355200\cdot t^{99}-3362679435315200\cdot t^{97}+7385205401333760\cdot t^{95}-14274866717296640\cdot t^{93}+24466298003443520\cdot t^{91}-37412057626624800\cdot t^{89}+51297485177122800\cdot t^{87}-63334617837497160\cdot t^{85}+\frac{565261464199662153}{8}\cdot t^{83}-\frac{1142949948111378673}{16}\cdot t^{81}+\frac{1049647911530857965}{16}\cdot t^{79}-\frac{1754728820090381655}{32}\cdot t^{77}+\frac{171144550919481890751}{4096}\cdot t^{75}-\frac{238058209925595111195}{8192}\cdot t^{73}+\frac{302522715514731118095}{16384}\cdot t^{71}-\frac{351458133732635263425}{32768}\cdot t^{69}+\frac{5974788273454799478225}{1048576}\cdot t^{67}-\frac{5806706317630136987409}{2097152}\cdot t^{65}+\frac{645189590847792998601}{524288}\cdot t^{63}-\frac{524367570089779328451}{1048576}\cdot t^{61}+\frac{6231121125092832279645}{33554432}\cdot t^{59}-\frac{4225702831959506948265}{67108864}\cdot t^{57}+\frac{2614039426281927554043}{134217728}\cdot t^{55}-\frac{1473187304754710594973}{268435456}\cdot t^{53}+\frac{48334573951237885711257}{34359738368}\cdot t^{51}-\frac{22499664763719716787825}{68719476736}\cdot t^{49}+\frac{4745266456623814014075}{68719476736}\cdot t^{47}-\frac{1809394370232925202545}{137438953472}\cdot t^{45}+\frac{19903338072562177227995}{8796093022208}\cdot t^{43}-\frac{6148721956730634976695}{17592186044416}\cdot t^{41}+\frac{1701063429324939500975}{35184372088832}\cdot t^{39}-\frac{419742924119140915825}{70368744177664}\cdot t^{37}+\frac{1471309407701830789155}{2251799813685248}\cdot t^{35}-\frac{284692389457752624243}{4503599627370496}\cdot t^{33}+\frac{12091182563842775547}{2251799813685248}\cdot t^{31}-\frac{1791143641983717945}{4503599627370496}\cdot t^{29}+\frac{3672749084067623665}{144115188075855872}\cdot t^{27}-\frac{403485110644048797}{288230376151711744}\cdot t^{25}+\frac{37591780494787155}{576460752303423488}\cdot t^{23}-\frac{2932692095338005}{1152921504606846976}\cdot t^{21}+\frac{6037895490401775}{73786976294838206464}\cdot t^{19}-\frac{314492881163175}{147573952589676412928}\cdot t^{17}+\frac{6480459369423}{147573952589676412928}\cdot t^{15}-\frac{205263418941}{295147905179352825856}\cdot t^{13}+\frac{615790256823}{75557863725914323419136}\cdot t^{11}-\frac{10143295635}{151115727451828646838272}\cdot t^9+\frac{109067695}{302231454903657293676544}\cdot t^7-\frac{682689}{604462909807314587353088}\cdot t^5+\frac{32509}{19342813113834066795298816}\cdot t^3-\frac{29}{38685626227668133590597632}\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.