Rule: Q[9, 10, 20, 40, 80]

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.

• $P_1$:
  $512\cdot t^9-1024\cdot t^7+672\cdot t^5-160\cdot t^3+10\cdot t$
• $P_2$:
  $512\cdot t^{19}-2304\cdot t^{17}+4352\cdot t^{15}-4480\cdot t^{13}+2730\cdot t^{11}-1001\cdot t^9+\frac{429}{2}\cdot t^7-\frac{99}{4}\cdot t^5+\frac{165}{128}\cdot t^3-\frac{5}{256}\cdot t$
• $P_3$:
  $512\cdot t^{39}-4864\cdot t^{37}+21312\cdot t^{35}-57120\cdot t^{33}+104720\cdot t^{31}-139128\cdot t^{29}+138446\cdot t^{27}-105183\cdot t^{25}+\frac{7888725}{128}\cdot t^{23}-\frac{7153575}{256}\cdot t^{21}+\frac{10015005}{1024}\cdot t^{19}-\frac{5368545}{2048}\cdot t^{17}+\frac{4345965}{8192}\cdot t^{15}-\frac{1300075}{16384}\cdot t^{13}+\frac{557175}{65536}\cdot t^{11}-\frac{81719}{131072}\cdot t^9+\frac{245157}{8388608}\cdot t^7-\frac{13167}{16777216}\cdot t^5+\frac{665}{67108864}\cdot t^3-\frac{5}{134217728}\cdot t$
• $P_4$:
  $512\cdot t^{79}-9984\cdot t^{77}+93632\cdot t^{75}-562400\cdot t^{73}+2430900\cdot t^{71}-8054382\cdot t^{69}+\frac{42557613}{2}\cdot t^{67}-\frac{184138713}{4}\cdot t^{65}+\frac{1329890705}{16}\cdot t^{63}-\frac{4064595535}{32}\cdot t^{61}+\frac{21252028083}{128}\cdot t^{59}-\frac{47908063307}{256}\cdot t^{57}+\frac{374810142343}{2048}\cdot t^{55}-\frac{639027625005}{4096}\cdot t^{53}+\frac{1906017461595}{16384}\cdot t^{51}-\frac{2492484372855}{32768}\cdot t^{49}+\frac{366395202809685}{8388608}\cdot t^{47}-\frac{369816259792035}{16777216}\cdot t^{45}+\frac{656125622211675}{67108864}\cdot t^{43}-\frac{511200549488475}{134217728}\cdot t^{41}+\frac{1397281501935165}{1073741824}\cdot t^{39}-\frac{835662302610135}{2147483648}\cdot t^{37}+\frac{872337137207445}{8589934592}\cdot t^{35}-\frac{395911973027025}{17179869184}\cdot t^{33}+\frac{622147386185325}{137438953472}\cdot t^{31}-\frac{210398934237219}{274877906944}\cdot t^{29}+\frac{121683714103007}{1099511627776}\cdot t^{27}-\frac{29846948742247}{2199023255552}\cdot t^{25}+\frac{24599133578775}{17592186044416}\cdot t^{23}-\frac{4207965378925}{35184372088832}\cdot t^{21}+\frac{1178230306099}{140737488355328}\cdot t^{19}-\frac{132638171391}{281474976710656}\cdot t^{17}+\frac{751616304549}{36028797018963968}\cdot t^{15}-\frac{50883115395}{72057594037927936}\cdot t^{13}+\frac{5075297955}{288230376151711744}\cdot t^{11}-\frac{177232627}{576460752303423488}\cdot t^9+\frac{16112057}{4611686018427387904}\cdot t^7-\frac{212667}{9223372036854775808}\cdot t^5+\frac{2665}{36893488147419103232}\cdot t^3-\frac{5}{73786976294838206464}\cdot t$
• $P_5$:
  $512\cdot t^{159}-20224\cdot t^{157}+391872\cdot t^{155}-4964960\cdot t^{153}+46260060\cdot t^{151}-337996890\cdot t^{149}+\frac{4033283235}{2}\cdot t^{147}-\frac{40411916335}{4}\cdot t^{145}+\frac{2775660569325}{64}\cdot t^{143}-\frac{20736778337275}{128}\cdot t^{141}+\frac{272896002918539}{512}\cdot t^{139}-\frac{1596916146425691}{1024}\cdot t^{137}+\frac{33506465811039949}{8192}\cdot t^{135}-\frac{158590258116617655}{16384}\cdot t^{133}+\frac{1362138244371496845}{65536}\cdot t^{131}-\frac{5332692942907262361}{131072}\cdot t^{129}+\frac{76435265515004093841}{1048576}\cdot t^{127}-\frac{251566663671553992111}{2097152}\cdot t^{125}+\frac{1525541192061458089875}{8388608}\cdot t^{123}-\frac{4272540337453198972875}{16777216}\cdot t^{121}+\frac{44312346928443177918675}{134217728}\cdot t^{119}-\frac{106583414794312967511825}{268435456}\cdot t^{117}+\frac{476465779179320024726775}{1073741824}\cdot t^{115}-\frac{991187934789096401803875}{2147483648}\cdot t^{113}+\frac{15373130518003436349546375}{34359738368}\cdot t^{111}-\frac{27808284981455104863401665}{68719476736}\cdot t^{109}+\frac{93960714925858063849587945}{274877906944}\cdot t^{107}-\frac{148385189179766382648569545}{549755813888}\cdot t^{105}+\frac{876821572425892261105183675}{4398046511104}\cdot t^{103}-\frac{1212409507752885508709010225}{8796093022208}\cdot t^{101}+\frac{3139829750847216317425898275}{35184372088832}\cdot t^{99}-\frac{3808780725521341924439367975}{70368744177664}\cdot t^{97}+\frac{1108355191126710500011856080725}{36028797018963968}\cdot t^{95}-\frac{1180817448909750031627997470875}{72057594037927936}\cdot t^{93}+\frac{2358327285917792079974123800375}{288230376151711744}\cdot t^{91}-\frac{2207394339619053386855779877151}{576460752303423488}\cdot t^{89}+\frac{7745659707838900594020818995451}{4611686018427387904}\cdot t^{87}-\frac{6367065033404818088822650815641}{9223372036854775808}\cdot t^{85}+\frac{9806049253345643044476645130215}{36893488147419103232}\cdot t^{83}-\frac{7071410385491676897722827585955}{73786976294838206464}\cdot t^{81}+\frac{38185616081655055247703268964157}{1180591620717411303424}\cdot t^{79}-\frac{24113523908091663295383023504523}{2361183241434822606848}\cdot t^{77}+\frac{28473031055317274738616112499691}{9444732965739290427392}\cdot t^{75}-\frac{15705160242199450884448362589275}{18889465931478580854784}\cdot t^{73}+\frac{32345737552116110442265122950325}{151115727451828646838272}\cdot t^{71}-\frac{15532204409083774772759194305615}{302231454903657293676544}\cdot t^{69}+\frac{13897235523917061638784542273445}{1208925819614629174706176}\cdot t^{67}-\frac{5785499480960388492440712288945}{2417851639229258349412352}\cdot t^{65}+\frac{17907498393448821524221252322925}{38685626227668133590597632}\cdot t^{63}-\frac{6430105600736449427616125351475}{77371252455336267181195264}\cdot t^{61}+\frac{4278942999762800891831821597527}{309485009821345068724781056}\cdot t^{59}-\frac{1317012317430140731412888424783}{618970019642690137449562112}\cdot t^{57}+\frac{1497116565967595874170206499967}{4951760157141521099596496896}\cdot t^{55}-\frac{392032816163265715595619229845}{9903520314283042199192993792}\cdot t^{53}+\frac{188756541115646455657149999555}{39614081257132168796771975168}\cdot t^{51}-\frac{41673522064493373326903246655}{79228162514264337593543950336}\cdot t^{49}+\frac{67318766411873910758843706135}{1267650600228229401496703205376}\cdot t^{47}-\frac{12395092231516896189799019985}{2535301200456458802993406410752}\cdot t^{45}+\frac{4148458860446831381981416425}{10141204801825835211973625643008}\cdot t^{43}-\frac{628638756667811501582349225}{20282409603651670423947251286016}\cdot t^{41}+\frac{343655853645070287531684243}{162259276829213363391578010288128}\cdot t^{39}-\frac{42167409761715032796982617}{324518553658426726783156020576256}\cdot t^{37}+\frac{9244073371067219171425419}{1298074214633706907132624082305024}\cdot t^{35}-\frac{900052962818686860906255}{2596148429267413814265248164610048}\cdot t^{33}+\frac{9900582591005555469968805}{664613997892457936451903530140172288}\cdot t^{31}-\frac{745549944100013488831659}{1329227995784915872903807060280344576}\cdot t^{29}+\frac{97580037815798025939927}{5316911983139663491615228241121378304}\cdot t^{27}-\frac{5496805211578415519967}{10633823966279326983230456482242756608}\cdot t^{25}+\frac{1054374401197905790275}{85070591730234615865843651857942052864}\cdot t^{23}-\frac{42483950231417449425}{170141183460469231731687303715884105728}\cdot t^{21}+\frac{2832263348761163295}{680564733841876926926749214863536422912}\cdot t^{19}-\frac{76644569178376155}{1361129467683753853853498429727072845824}\cdot t^{17}+\frac{13161188646791865}{21778071482940061661655974875633165533184}\cdot t^{15}-\frac{217591687594575}{43556142965880123323311949751266331066368}\cdot t^{13}+\frac{5333800010175}{174224571863520493293247799005065324265472}\cdot t^{11}-\frac{46017098127}{348449143727040986586495598010130648530944}\cdot t^9+\frac{1037979657}{2787593149816327892691964784081045188247552}\cdot t^7-\frac{3410667}{5575186299632655785383929568162090376495104}\cdot t^5+\frac{10665}{22300745198530623141535718272648361505980416}\cdot t^3-\frac{5}{44601490397061246283071436545296723011960832}\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.