Rule: Q[1, 82, 84]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{83}-\frac{83}{4}\cdot t^{81}+\frac{415}{2}\cdot t^{79}-\frac{85241}{64}\cdot t^{77}+\frac{1578577}{256}\cdot t^{75}-\frac{22464365}{1024}\cdot t^{73}+\frac{63892155}{1024}\cdot t^{71}-\frac{1193774475}{8192}\cdot t^{69}+\frac{18670632789}{65536}\cdot t^{67}-\frac{123966273563}{262144}\cdot t^{65}+\frac{22076185703}{32768}\cdot t^{63}-\frac{435502936141}{524288}\cdot t^{61}+\frac{1870822472155}{2097152}\cdot t^{59}-\frac{7035114834851}{8388608}\cdot t^{57}+\frac{5811616602703}{8388608}\cdot t^{55}-\frac{33844120215741}{67108864}\cdot t^{53}+\frac{348038788487247}{1073741824}\cdot t^{51}-\frac{790997246561925}{4294967296}\cdot t^{49}+\frac{198763410674535}{2147483648}\cdot t^{47}-\frac{11308591944166965}{274877906944}\cdot t^{45}+\frac{17770644483690945}{1099511627776}\cdot t^{43}-\frac{24649603638668085}{4398046511104}\cdot t^{41}+\frac{7530802900040175}{4398046511104}\cdot t^{39}-\frac{16174854924434115}{35184372088832}\cdot t^{37}+\frac{30430659264613335}{281474976710656}\cdot t^{35}-\frac{24974127258544737}{1125899906842624}\cdot t^{33}+\frac{1112208096534381}{281474976710656}\cdot t^{31}-\frac{2736384999409985}{4503599627370496}\cdot t^{29}+\frac{1442821181507083}{18014398509481984}\cdot t^{27}-\frac{646781908951451}{72057594037927936}\cdot t^{25}+\frac{61017161221835}{72057594037927936}\cdot t^{23}-\frac{38306059030085}{576460752303423488}\cdot t^{21}+\frac{78865415650175}{18446744073709551616}\cdot t^{19}-\frac{16346649789309}{73786976294838206464}\cdot t^{17}+\frac{333605097741}{36893488147419103232}\cdot t^{15}-\frac{333605097741}{1180591620717411303424}\cdot t^{13}+\frac{30757916813}{4722366482869645213696}\cdot t^{11}-\frac{1987879465}{18889465931478580854784}\cdot t^9+\frac{20925047}{18889465931478580854784}\cdot t^7-\frac{1024303}{151115727451828646838272}\cdot t^5+\frac{23821}{1208925819614629174706176}\cdot t^3-\frac{83}{4835703278458516698824704}\cdot t$
• $P_3$:
  $t^{167}-42\cdot t^{165}+\frac{13859}{16}\cdot t^{163}-\frac{187083}{16}\cdot t^{161}+\frac{3718295}{32}\cdot t^{159}-\frac{1812971}{2}\cdot t^{157}+\frac{23680043257}{4096}\cdot t^{155}-\frac{126954590191}{4096}\cdot t^{153}+\frac{9342540624417}{65536}\cdot t^{151}-\frac{18718442131675}{32768}\cdot t^{149}+\frac{2116663008444765}{1048576}\cdot t^{147}-\frac{6660489990753025}{1048576}\cdot t^{145}+\frac{75249453342666435}{4194304}\cdot t^{143}-\frac{48011094318382405}{1048576}\cdot t^{141}+\frac{14250685160198912075}{134217728}\cdot t^{139}-\frac{30169635929927724545}{134217728}\cdot t^{137}+\frac{1873600195307812851061}{4294967296}\cdot t^{135}-\frac{1672472338652681756757}{2147483648}\cdot t^{133}+\frac{88167577970088201911403}{68719476736}\cdot t^{131}-\frac{134388237280860133554555}{68719476736}\cdot t^{129}+\frac{94985370866259994497663}{34359738368}\cdot t^{127}-\frac{15597763640527754914371}{4294967296}\cdot t^{125}+\frac{9767590619576066456558925}{2199023255552}\cdot t^{123}-\frac{11140306595931867587195475}{2199023255552}\cdot t^{121}+\frac{189842209414339972888360875}{35184372088832}\cdot t^{119}-\frac{94523817369075964070769645}{17592186044416}\cdot t^{117}+\frac{2819306657346089425695986355}{562949953421312}\cdot t^{115}-\frac{2461926373047738186362974135}{562949953421312}\cdot t^{113}+\frac{8063117983996031502958200855}{2251799813685248}\cdot t^{111}-\frac{1548633801553448081185989275}{562949953421312}\cdot t^{109}+\frac{142974110714859397428480473085}{72057594037927936}\cdot t^{107}-\frac{96863507703796930986052261615}{72057594037927936}\cdot t^{105}+\frac{3946541126404587885944139024655}{4611686018427387904}\cdot t^{103}-\frac{1180774745263496777790372760355}{2305843009213693952}\cdot t^{101}+\frac{21256617623579574324605993315125}{73786976294838206464}\cdot t^{99}-\frac{11244099729519275422857133004925}{73786976294838206464}\cdot t^{97}+\frac{11185628592565168058646093601375}{147573952589676412928}\cdot t^{95}-\frac{20435677857579594006371430225}{576460752303423488}\cdot t^{93}+\frac{1177835867795643889054979740585525}{75557863725914323419136}\cdot t^{91}-\frac{486865430060505095816108906503875}{75557863725914323419136}\cdot t^{89}+\frac{3026074741477263010548942188623825}{1208925819614629174706176}\cdot t^{87}-\frac{552181781702690721784089081464963}{604462909807314587353088}\cdot t^{85}+\frac{6055749064139919351742848573128869}{19342813113834066795298816}\cdot t^{83}-\frac{1948026357141046863631120890019993}{19342813113834066795298816}\cdot t^{81}+\frac{2351396658051416774140133190201495}{77371252455336267181195264}\cdot t^{79}-\frac{166302313464332427223197131094501}{19342813113834066795298816}\cdot t^{77}+\frac{5641337381109518695057071774898563}{2475880078570760549798248448}\cdot t^{75}-\frac{1399390136323816714617183964173945}{2475880078570760549798248448}\cdot t^{73}+\frac{10387940835546234797669199508414455}{79228162514264337593543950336}\cdot t^{71}-\frac{1125595855342612501389338138790975}{39614081257132168796771975168}\cdot t^{69}+\frac{7284018459548215478432626828393041}{1267650600228229401496703205376}\cdot t^{67}-\frac{1372872865909877439200172790852977}{1267650600228229401496703205376}\cdot t^{65}+\frac{240837448141437015611814297659829}{1267650600228229401496703205376}\cdot t^{63}-\frac{4908180358780189419320322684831}{158456325028528675187087900672}\cdot t^{61}+\frac{380161674762673820933426898956865}{81129638414606681695789005144064}\cdot t^{59}-\frac{53268592537064371344127581508047}{81129638414606681695789005144064}\cdot t^{57}+\frac{110403267192203384154778112217243}{1298074214633706907132624082305024}\cdot t^{55}-\frac{6596530489769834055306063793797}{649037107316853453566312041152512}\cdot t^{53}+\frac{23216757365885354426171262997803}{20769187434139310514121985316880384}\cdot t^{51}-\frac{2344307071219453808858292038175}{20769187434139310514121985316880384}\cdot t^{49}+\frac{866888480808132493123288739955}{83076749736557242056487941267521536}\cdot t^{47}-\frac{18287247197690251696220234475}{20769187434139310514121985316880384}\cdot t^{45}+\frac{179683005602990977325552260485}{2658455991569831745807614120560689152}\cdot t^{43}-\frac{12501309576902058321956719095}{2658455991569831745807614120560689152}\cdot t^{41}+\frac{100493440332830641061783762175}{340282366920938463463374607431768211456}\cdot t^{39}-\frac{2835500458967930927480899515}{170141183460469231731687303715884105728}\cdot t^{37}+\frac{4577712538856953945070233773}{5444517870735015415413993718908291383296}\cdot t^{35}-\frac{205302390825703489742014437}{5444517870735015415413993718908291383296}\cdot t^{33}+\frac{16265276694365372372939253}{10889035741470030830827987437816582766592}\cdot t^{31}-\frac{35311170792370456830255}{680564733841876926926749214863536422912}\cdot t^{29}+\frac{2184426037978321443810573}{1393796574908163946345982392040522594123776}\cdot t^{27}-\frac{56833057277264544803163}{1393796574908163946345982392040522594123776}\cdot t^{25}+\frac{20152104947983707185565}{22300745198530623141535718272648361505980416}\cdot t^{23}-\frac{187734305562463131615}{11150372599265311570767859136324180752990208}\cdot t^{21}+\frac{92647108943288724825}{356811923176489970264571492362373784095686656}\cdot t^{19}-\frac{1160549928812604429}{356811923176489970264571492362373784095686656}\cdot t^{17}+\frac{46147175847959967}{1427247692705959881058285969449495136382746624}\cdot t^{15}-\frac{88375564755441}{356811923176489970264571492362373784095686656}\cdot t^{13}+\frac{64268475123951}{45671926166590716193865151022383844364247891968}\cdot t^{11}-\frac{257130050445}{45671926166590716193865151022383844364247891968}\cdot t^9+\frac{21525605037}{1461501637330902918203684832716283019655932542976}\cdot t^7-\frac{16412669}{730750818665451459101842416358141509827966271488}\cdot t^5+\frac{381219}{23384026197294446691258957323460528314494920687616}\cdot t^3-\frac{83}{23384026197294446691258957323460528314494920687616}\cdot t$

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.