Rule: Q[22, 23, 92]

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.

• $P_1$:
  $4194304\cdot t^{22}-22020096\cdot t^{20}+49807360\cdot t^{18}-63504384\cdot t^{16}+50135040\cdot t^{14}-25346048\cdot t^{12}+8200192\cdot t^{10}-1647360\cdot t^8+192192\cdot t^6-11440\cdot t^4+264\cdot t^2-1$
• $P_2$:
  $4194304\cdot t^{45}-46137344\cdot t^{43}+236716032\cdot t^{41}-752353280\cdot t^{39}+1659207680\cdot t^{37}-2695200768\cdot t^{35}+3340925952\cdot t^{33}-3230785536\cdot t^{31}+2470913280\cdot t^{29}-1506292480\cdot t^{27}+734317584\cdot t^{25}-286097760\cdot t^{23}+88704330\cdot t^{21}-21710850\cdot t^{19}+\frac{265182525}{64}\cdot t^{17}-\frac{9694845}{16}\cdot t^{15}+\frac{67863915}{1024}\cdot t^{13}-\frac{5368545}{1024}\cdot t^{11}+\frac{4686825}{16384}\cdot t^9-\frac{82225}{8192}\cdot t^7+\frac{26565}{131072}\cdot t^5-\frac{253}{131072}\cdot t^3+\frac{23}{4194304}\cdot t$
• $P_3$:
  $4194304\cdot t^{137}-142606336\cdot t^{135}+2371092480\cdot t^{133}-25695617024\cdot t^{131}+204102778880\cdot t^{129}-1266971836416\cdot t^{127}+6399647514624\cdot t^{125}-27043221504000\cdot t^{123}+97550620646400\cdot t^{121}-305003232512000\cdot t^{119}+836495193541700\cdot t^{117}-2031659407077300\cdot t^{115}+\frac{17615777001840875}{4}\cdot t^{113}-8574818220588389\cdot t^{111}+\frac{241240853625309285}{16}\cdot t^{109}-\frac{384808581148664079}{16}\cdot t^{107}+\frac{35774581372033999869}{1024}\cdot t^{105}-\frac{23739573929424603705}{512}\cdot t^{103}+\frac{923733198898277357499}{16384}\cdot t^{101}-\frac{1031590591427753351475}{16384}\cdot t^{99}+\frac{16963545623783157654255}{262144}\cdot t^{97}-\frac{2009113462157468000565}{32768}\cdot t^{95}+\frac{28121290308881174365275}{524288}\cdot t^{93}-\frac{22741565206312601878005}{524288}\cdot t^{91}+\frac{544600640466959676552225}{16777216}\cdot t^{89}-\frac{188730629032620716228187}{8388608}\cdot t^{87}+\frac{7758695419901473619886237}{536870912}\cdot t^{85}-\frac{4621044819661037841673985}{536870912}\cdot t^{83}+\frac{40845235120276653961601483}{8589934592}\cdot t^{81}-\frac{5233255369728581099161215}{2147483648}\cdot t^{79}+\frac{39811505664527798435841243}{34359738368}\cdot t^{77}-\frac{17559310457402523096664377}{34359738368}\cdot t^{75}+\frac{919378990930037765910257475}{4398046511104}\cdot t^{73}-\frac{174323808669851316653113755}{2199023255552}\cdot t^{71}+\frac{1960156853142898289063292675}{70368744177664}\cdot t^{69}-\frac{637798609913070649950413955}{70368744177664}\cdot t^{67}+\frac{3072271735332895875904935195}{1125899906842624}\cdot t^{65}-\frac{53437961679592783498480275}{70368744177664}\cdot t^{63}+\frac{219714398232094118257962057}{1125899906842624}\cdot t^{61}-\frac{52069068734101558716921855}{1125899906842624}\cdot t^{59}+\frac{363633373894072518223074669}{36028797018963968}\cdot t^{57}-\frac{36482201705741748748053003}{18014398509481984}\cdot t^{55}+\frac{859937611635341220489820785}{2305843009213693952}\cdot t^{53}-\frac{145042108792350085903913469}{2305843009213693952}\cdot t^{51}+\frac{357695722843803403341372675}{36893488147419103232}\cdot t^{49}-\frac{12564222522828936748191585}{9223372036854775808}\cdot t^{47}+\frac{25674715590128696833261065}{147573952589676412928}\cdot t^{45}-\frac{2971471643000632436863275}{147573952589676412928}\cdot t^{43}+\frac{19875843656515341411018795}{9444732965739290427392}\cdot t^{41}-\frac{934315053791709467841975}{4722366482869645213696}\cdot t^{39}+\frac{2517554381307842602439649}{151115727451828646838272}\cdot t^{37}-\frac{188944243627566280507641}{151115727451828646838272}\cdot t^{35}+\frac{201112388118787006980405}{2417851639229258349412352}\cdot t^{33}-\frac{1473187304754710594973}{302231454903657293676544}\cdot t^{31}+\frac{1208169482735344667835}{4835703278458516698824704}\cdot t^{29}-\frac{53725828038395392677}{4835703278458516698824704}\cdot t^{27}+\frac{65706500492950462821}{154742504910672534362390528}\cdot t^{25}-\frac{1067357058040130975}{77371252455336267181195264}\cdot t^{23}+\frac{1862354039201056115}{4951760157141521099596496896}\cdot t^{21}-\frac{41953909915492575}{4951760157141521099596496896}\cdot t^{19}+\frac{12263450590682445}{79228162514264337593543950336}\cdot t^{17}-\frac{44385492876645}{19807040628566084398385987584}\cdot t^{15}+\frac{7912524197025}{316912650057057350374175801344}\cdot t^{13}-\frac{65309723531}{316912650057057350374175801344}\cdot t^{11}+\frac{97082021465}{81129638414606681695789005144064}\cdot t^9-\frac{184138713}{40564819207303340847894502572032}\cdot t^7+\frac{13019909}{1298074214633706907132624082305024}\cdot t^5-\frac{13685}{1298074214633706907132624082305024}\cdot t^3+\frac{69}{20769187434139310514121985316880384}\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.