Rule: Q[40, 82]

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.

• $P_1$:
  $1099511627776\cdot t^{40}-10720238370816\cdot t^{38}+48309792145408\cdot t^{36}-133487583559680\cdot t^{34}+252995048570880\cdot t^{32}-348570955808768\cdot t^{30}+361019918516224\cdot t^{28}-286692288233472\cdot t^{26}+176467791052800\cdot t^{24}-84557483212800\cdot t^{22}+31504481648640\cdot t^{20}-9069471989760\cdot t^{18}+1993720135680\cdot t^{16}-328635187200\cdot t^{14}+39557939200\cdot t^{12}-3347210240\cdot t^{10}+188280576\cdot t^8-6460608\cdot t^6+117040\cdot t^4-840\cdot t^2+1$
• $P_2$:
  $1099511627776\cdot t^{122}-33260226740224\cdot t^{120}+490657063895040\cdot t^{118}-4704174600093696\cdot t^{116}+32958870359900160\cdot t^{114}-179905155922132992\cdot t^{112}+796503168954400768\cdot t^{110}-2940293410025635840\cdot t^{108}+9233160501700067328\cdot t^{106}-25040223290429276160\cdot t^{104}+59343113249353629696\cdot t^{102}-124056970920219377664\cdot t^{100}+230511263534191411200\cdot t^{98}-383083928523780341760\cdot t^{96}+572366551136447692800\cdot t^{94}-772164875005374341120\cdot t^{92}+944007642164864775680\cdot t^{90}-1049042898687648009600\cdot t^{88}+1062364078353522904960\cdot t^{86}-982525482384141249400\cdot t^{84}+831331027085222426070\cdot t^{82}-\frac{1288912390732970904285}{2}\cdot t^{80}+458254180323603516825\cdot t^{78}-\frac{2393282266977011062653}{8}\cdot t^{76}+\frac{11482919967818992472325}{64}\cdot t^{74}-\frac{25318666802513549932857}{256}\cdot t^{72}+\frac{12829998482796319117443}{256}\cdot t^{70}-\frac{382524028838927292205245}{16384}\cdot t^{68}+\frac{655180253906072459882367}{65536}\cdot t^{66}-\frac{1031079709925550569660805}{262144}\cdot t^{64}+\frac{46564890125670025726617}{32768}\cdot t^{62}-\frac{123498186855037894318419}{262144}\cdot t^{60}+\frac{1201053795238555345843965}{8388608}\cdot t^{58}-\frac{1336930588235240395070757}{33554432}\cdot t^{56}+\frac{340197142412800761468765}{33554432}\cdot t^{54}-\frac{1264473015046020492628059}{536870912}\cdot t^{52}+\frac{1070684047222875589543299}{2147483648}\cdot t^{50}-\frac{824379608955388181766525}{8589934592}\cdot t^{48}+\frac{71973699605393023918935}{4294967296}\cdot t^{46}-\frac{90955774226595579677775}{34359738368}\cdot t^{44}+\frac{103667665564288455873705}{274877906944}\cdot t^{42}-\frac{53098072606098965203605}{1099511627776}\cdot t^{40}+\frac{6087080633856142395475}{1099511627776}\cdot t^{38}-\frac{19903338072562177227995}{35184372088832}\cdot t^{36}+\frac{7214673754726220744325}{140737488355328}\cdot t^{34}-\frac{2306229046382569708015}{562949953421312}\cdot t^{32}+\frac{40368774950795968915}{140737488355328}\cdot t^{30}-\frac{19664520832694564925}{1125899906842624}\cdot t^{28}+\frac{16518197499463434537}{18014398509481984}\cdot t^{26}-\frac{2961066843533158425}{72057594037927936}\cdot t^{24}+\frac{111952664221253661}{72057594037927936}\cdot t^{22}-\frac{56342190490434849}{1152921504606846976}\cdot t^{20}+\frac{5799033690781485}{4611686018427387904}\cdot t^{18}-\frac{478303048350171}{18446744073709551616}\cdot t^{16}+\frac{3851071242755}{9223372036854775808}\cdot t^{14}-\frac{374810142343}{73786976294838206464}\cdot t^{12}+\frac{26372568651}{590295810358705651712}\cdot t^{10}-\frac{630922695}{2361183241434822606848}\cdot t^8+\frac{2342949}{2361183241434822606848}\cdot t^6-\frac{595665}{302231454903657293676544}\cdot t^4+\frac{1891}{1208925819614629174706176}\cdot t^2-\frac{1}{4835703278458516698824704}$

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.