Rule: Q[42, 86]

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.

• $P_1$:
  $4398046511104\cdot t^{42}-45079976738816\cdot t^{40}+214404767416320\cdot t^{38}-628027297890304\cdot t^{36}+1268132043816960\cdot t^{34}-1872163359424512\cdot t^{32}+2091425734852608\cdot t^{30}-1805099592581120\cdot t^{28}+1218442224992256\cdot t^{26}-647048567193600\cdot t^{24}+270583946280960\cdot t^{22}-88785357373440\cdot t^{20}+22673679974400\cdot t^{18}-4447529533440\cdot t^{16}+657270374400\cdot t^{14}-71204290560\cdot t^{12}+5439216640\cdot t^{10}-276883200\cdot t^8+8614144\cdot t^6-141680\cdot t^4+924\cdot t^2-1$
• $P_2$:
  $4398046511104\cdot t^{128}-139637976727552\cdot t^{126}+2164663517184000\cdot t^{124}-21835613732864000\cdot t^{122}+161168664962269184\cdot t^{120}-928019570831130624\cdot t^{118}+4340189090411446272\cdot t^{116}-16949099082578657280\cdot t^{114}+56389022309343559680\cdot t^{112}-162275075312444243968\cdot t^{110}+408755914495001362432\cdot t^{108}-909781076252741861376\cdot t^{106}+1803038350906876231680\cdot t^{104}-3201947416265659514880\cdot t^{102}+5122121472417519304704\cdot t^{100}-7413596867972725309440\cdot t^{98}+9744697431823662443520\cdot t^{96}-11669070454074553766400\cdot t^{94}+12764140879569538166400\cdot t^{92}-12782462612889494441280\cdot t^{90}+11741688707482207623240\cdot t^{88}-9908991263721757227020\cdot t^{86}+7692727924575833191325\cdot t^{84}-\frac{10999528115287676171025}{2}\cdot t^{82}+\frac{115966453558318643060235}{32}\cdot t^{80}-\frac{140943843555494966180901}{64}\cdot t^{78}+\frac{316097357876886768813477}{256}\cdot t^{76}-\frac{327116002160176939403925}{512}\cdot t^{74}+\frac{1249703425508681631301275}{4096}\cdot t^{72}-\frac{1101462743310410430898641}{8192}\cdot t^{70}+\frac{1791267693666425044188699}{32768}\cdot t^{68}-\frac{1343155959898655777044719}{65536}\cdot t^{66}+\frac{29701747773016666409906415}{4194304}\cdot t^{64}-\frac{18901112219192424079031355}{8388608}\cdot t^{62}+\frac{22131271335289705221949407}{33554432}\cdot t^{60}-\frac{11906489441781999465911991}{67108864}\cdot t^{58}+\frac{23514249757784522242715079}{536870912}\cdot t^{56}-\frac{10638056588421904892415165}{1073741824}\cdot t^{54}+\frac{8804545389260697455781435}{4294967296}\cdot t^{52}-\frac{3326161591498485705517431}{8589934592}\cdot t^{50}+\frac{9156287527158752784851355}{137438953472}\cdot t^{48}-\frac{2862608739089543553578805}{274877906944}\cdot t^{46}+\frac{1621674901454667530352525}{1099511627776}\cdot t^{44}-\frac{414847067813984717066925}{2199023255552}\cdot t^{42}+\frac{382014251751701434646655}{17592186044416}\cdot t^{40}-\frac{78828337663049502387405}{35184372088832}\cdot t^{38}+\frac{29028979244171713032135}{140737488355328}\cdot t^{36}-\frac{4745266456623814014075}{281474976710656}\cdot t^{34}+\frac{10955121325785842230025}{9007199254740992}\cdot t^{32}-\frac{1386158208568820853595}{18014398509481984}\cdot t^{30}+\frac{305305732013892188007}{72057594037927936}\cdot t^{28}-\frac{29010951910822334607}{144115188075855872}\cdot t^{26}+\frac{9419140230786472275}{1152921504606846976}\cdot t^{24}-\frac{645402855932737425}{2305843009213693952}\cdot t^{22}+\frac{73623733195290047}{9223372036854775808}\cdot t^{20}-\frac{3436980173735899}{18446744073709551616}\cdot t^{18}+\frac{1029076255541277}{295147905179352825856}\cdot t^{16}-\frac{30089948992435}{590295810358705651712}\cdot t^{14}+\frac{1329861757315}{2361183241434822606848}\cdot t^{12}-\frac{21252028083}{4722366482869645213696}\cdot t^{10}+\frac{924001221}{37778931862957161709568}\cdot t^8-\frac{6237231}{75557863725914323419136}\cdot t^6+\frac{45045}{302231454903657293676544}\cdot t^4-\frac{65}{604462909807314587353088}\cdot t^2+\frac{1}{77371252455336267181195264}$

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.