Rule: Q[4, 8, 24, 72]

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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^{12}-24\cdot t^{10}+27\cdot t^8-14\cdot t^6+\frac{105}{32}\cdot t^4-\frac{9}{32}\cdot t^2+\frac{1}{256}$
• $P_3$:
  $8\cdot t^{36}-72\cdot t^{34}+297\cdot t^{32}-744\cdot t^{30}+\frac{40455}{32}\cdot t^{28}-\frac{49329}{32}\cdot t^{26}+\frac{356265}{256}\cdot t^{24}-\frac{121095}{128}\cdot t^{22}+\frac{3996135}{8192}\cdot t^{20}-\frac{1562275}{8192}\cdot t^{18}+\frac{3677355}{65536}\cdot t^{16}-\frac{200583}{16384}\cdot t^{14}+\frac{2028117}{1048576}\cdot t^{12}-\frac{223839}{1048576}\cdot t^{10}+\frac{130815}{8388608}\cdot t^8-\frac{2907}{4194304}\cdot t^6+\frac{8721}{536870912}\cdot t^4-\frac{81}{536870912}\cdot t^2+\frac{1}{4294967296}$
• $P_4$:
  $8\cdot t^{108}-216\cdot t^{106}+2835\cdot t^{104}-24102\cdot t^{102}+\frac{4774977}{32}\cdot t^{100}-\frac{22947705}{32}\cdot t^{98}+\frac{712878705}{256}\cdot t^{96}-\frac{287369775}{32}\cdot t^{94}+\frac{50243731461}{2048}\cdot t^{92}-\frac{118024837203}{2048}\cdot t^{90}+\frac{1929344787747}{16384}\cdot t^{88}-\frac{1730443263237}{8192}\cdot t^{86}+\frac{702752236347915}{2097152}\cdot t^{84}-\frac{991819552999527}{2097152}\cdot t^{82}+\frac{10011649652010423}{16777216}\cdot t^{80}-\frac{2834839865623023}{4194304}\cdot t^{78}+\frac{370131483324606003}{536870912}\cdot t^{76}-\frac{340942058007474825}{536870912}\cdot t^{74}+\frac{2273788885625159265}{4294967296}\cdot t^{72}-\frac{859225959736532685}{2147483648}\cdot t^{70}+\frac{37727830777522298805}{137438953472}\cdot t^{68}-\frac{23520525044114886885}{137438953472}\cdot t^{66}+\frac{106662846130288440525}{1099511627776}\cdot t^{64}-\frac{3437217036423617265}{68719476736}\cdot t^{62}+\frac{103171070093286670605}{4398046511104}\cdot t^{60}-\frac{44003082907257206499}{4398046511104}\cdot t^{58}+\frac{136467347177666345859}{35184372088832}\cdot t^{56}-\frac{24023744244810947945}{17592186044416}\cdot t^{54}+\frac{982227943266413328837}{2251799813685248}\cdot t^{52}-\frac{284250164288796175041}{2251799813685248}\cdot t^{50}+\frac{595224702997906520385}{18014398509481984}\cdot t^{48}-\frac{35159900763596489055}{4503599627370496}\cdot t^{46}+\frac{1915289331069598219575}{1152921504606846976}\cdot t^{44}-\frac{366033072159967659741}{1152921504606846976}\cdot t^{42}+\frac{501040501001163998469}{9223372036854775808}\cdot t^{40}-\frac{38239881681106449981}{4611686018427387904}\cdot t^{38}+\frac{331884405207627584403}{295147905179352825856}\cdot t^{36}-\frac{39795808009289185035}{295147905179352825856}\cdot t^{34}+\frac{33572102696558244819}{2361183241434822606848}\cdot t^{32}-\frac{386746630841064879}{295147905179352825856}\cdot t^{30}+\frac{1979232757833684969}{18889465931478580854784}\cdot t^{28}-\frac{136175824983824703}{18889465931478580854784}\cdot t^{26}+\frac{63863121384910575}{151115727451828646838272}\cdot t^{24}-\frac{1576585107534465}{75557863725914323419136}\cdot t^{22}+\frac{33108287258223765}{38685626227668133590597632}\cdot t^{20}-\frac{1109448779376105}{38685626227668133590597632}\cdot t^{18}+\frac{238072458968505}{309485009821345068724781056}\cdot t^{16}-\frac{1245583147725}{77371252455336267181195264}\cdot t^{14}+\frac{2518845920955}{9903520314283042199192993792}\cdot t^{12}-\frac{28751959665}{9903520314283042199192993792}\cdot t^{10}+\frac{1784604393}{79228162514264337593543950336}\cdot t^8-\frac{4297293}{39614081257132168796771975168}\cdot t^6+\frac{708345}{2535301200456458802993406410752}\cdot t^4-\frac{729}{2535301200456458802993406410752}\cdot t^2+\frac{1}{20282409603651670423947251286016}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.