Rule: Q[48, 96]

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.

• $P_1$:
  $140737488355328\cdot t^{48}-1688849860263936\cdot t^{46}+9499780463984640\cdot t^{44}-33284415996035072\cdot t^{42}+81414437990301696\cdot t^{40}-147682003796361216\cdot t^{38}+205992953708019712\cdot t^{36}-226089827240509440\cdot t^{34}+198181864190509056\cdot t^{32}-140025932533465088\cdot t^{30}+80146421910601728\cdot t^{28}-37217871599763456\cdot t^{26}+13999778090188800\cdot t^{24}-4246086541639680\cdot t^{22}+1030300410839040\cdot t^{20}-197734422282240\cdot t^{18}+29544303329280\cdot t^{16}-3363677798400\cdot t^{14}+283420999680\cdot t^{12}-16974397440\cdot t^{10}+682007040\cdot t^8-16839680\cdot t^6+220800\cdot t^4-1152\cdot t^2+1$
• $P_2$:
  $140737488355328\cdot t^{144}-5066549580791808\cdot t^{142}+89297936361455616\cdot t^{140}-1027031821273006080\cdot t^{138}+8668331970083684352\cdot t^{136}-57248408262854836224\cdot t^{134}+308055897361291935744\cdot t^{132}-1388660734403404627968\cdot t^{130}+5351066295024148807680\cdot t^{128}-17898546027142502678528\cdot t^{126}+52593675359607167385600\cdot t^{124}-137074288548313143705600\cdot t^{122}+319364054221937914675200\cdot t^{120}-669483073148748300288000\cdot t^{118}+1269626828007090526617600\cdot t^{116}-2188219881862349822361600\cdot t^{114}+3440997133563328907673600\cdot t^{112}-4953505831919789830963200\cdot t^{110}+6546796177768769849344000\cdot t^{108}-7963660697925884671475712\cdot t^{106}+8935034633862408910637568\cdot t^{104}-9263655729571634170610688\cdot t^{102}+8889174862709293519526016\cdot t^{100}-7905392664464786726851200\cdot t^{98}+6523321412187696408458985\cdot t^{96}-4999385821777461449171928\cdot t^{94}+3561329111308553454095583\cdot t^{92}-2359563732183856403742341\cdot t^{90}+\frac{46551983977321896044276235}{32}\cdot t^{88}-\frac{13358395402188022343140137}{16}\cdot t^{86}+\frac{57105187362569849899622457}{128}\cdot t^{84}-\frac{28414028425052597309461017}{128}\cdot t^{82}+\frac{13480426914228525094960005351}{131072}\cdot t^{80}-\frac{1453663289959122962737974915}{32768}\cdot t^{78}+\frac{4668824448927536103852554727}{262144}\cdot t^{76}-\frac{1743925252875947299604165265}{262144}\cdot t^{74}+\frac{19384123901308368955682511855}{8388608}\cdot t^{72}-\frac{3128682791850479354049286455}{4194304}\cdot t^{70}+\frac{7503246218787395868946401975}{33554432}\cdot t^{68}-\frac{2086983502612660291753345995}{33554432}\cdot t^{66}+\frac{68870455586217789627860417835}{4294967296}\cdot t^{64}-\frac{1027430429062685471597254635}{268435456}\cdot t^{62}+\frac{1814071840669970333137636335}{2147483648}\cdot t^{60}-\frac{369664650930905766711215325}{2147483648}\cdot t^{58}+\frac{2222020610868317208631414299}{68719476736}\cdot t^{56}-\frac{192026472544175561239751853}{34359738368}\cdot t^{54}+\frac{243824207817848472168664509}{274877906944}\cdot t^{52}-\frac{35458532525385728679057813}{274877906944}\cdot t^{50}+\frac{4826300260399724181316202325}{281474976710656}\cdot t^{48}-\frac{146188686727467477887343615}{70368744177664}\cdot t^{46}+\frac{128770460223769225202894163}{562949953421312}\cdot t^{44}-\frac{12841751567750968484286093}{562949953421312}\cdot t^{42}+\frac{36979090634894929314282027}{18014398509481984}\cdot t^{40}-\frac{1495111481195212775510055}{9007199254740992}\cdot t^{38}+\frac{865072733563979079163431}{72057594037927936}\cdot t^{36}-\frac{55668623303912851876707}{72057594037927936}\cdot t^{34}+\frac{405585684071365063673151}{9223372036854775808}\cdot t^{32}-\frac{2535421699175704168959}{1152921504606846976}\cdot t^{30}+\frac{884449429945013082195}{9223372036854775808}\cdot t^{28}-\frac{33332191876292616657}{9223372036854775808}\cdot t^{26}+\frac{34390356697762223535}{295147905179352825856}\cdot t^{24}-\frac{468681535087022205}{147573952589676412928}\cdot t^{22}+\frac{85181301813613005}{1180591620717411303424}\cdot t^{20}-\frac{1585777713559325}{1180591620717411303424}\cdot t^{18}+\frac{48524798034915345}{2417851639229258349412352}\cdot t^{16}-\frac{141747219186705}{604462909807314587353088}\cdot t^{14}+\frac{10022530649565}{4835703278458516698824704}\cdot t^{12}-\frac{64110004155}{4835703278458516698824704}\cdot t^{10}+\frac{8931734325}{154742504910672534362390528}\cdot t^8-\frac{12081573}{77371252455336267181195264}\cdot t^6+\frac{139941}{618970019642690137449562112}\cdot t^4-\frac{81}{618970019642690137449562112}\cdot t^2+\frac{1}{79228162514264337593543950336}$

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.