Rule: Q[13, 26, 40, 78]

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.

• $P_1$:
  $4096\cdot t^{13}-13312\cdot t^{11}+16640\cdot t^9-9984\cdot t^7+2912\cdot t^5-364\cdot t^3+13\cdot t$
• $P_2$:
  $4096\cdot t^{39}-39936\cdot t^{37}+179712\cdot t^{35}-495040\cdot t^{33}+933504\cdot t^{31}-1276704\cdot t^{29}+1308944\cdot t^{27}-\frac{4102137}{4}\cdot t^{25}+\frac{9924525}{16}\cdot t^{23}-\frac{18599295}{64}\cdot t^{21}+\frac{13468455}{128}\cdot t^{19}-\frac{29910465}{1024}\cdot t^{17}+\frac{6277505}{1024}\cdot t^{15}-\frac{3900225}{4096}\cdot t^{13}+\frac{869193}{8192}\cdot t^{11}-\frac{1062347}{131072}\cdot t^9+\frac{415701}{1048576}\cdot t^7-\frac{46683}{4194304}\cdot t^5+\frac{1235}{8388608}\cdot t^3-\frac{39}{67108864}\cdot t$
• $P_3$:
  $4096\cdot t^{79}-81920\cdot t^{77}+788224\cdot t^{75}-4859136\cdot t^{73}+21563616\cdot t^{71}-73381056\cdot t^{69}+199185175\cdot t^{67}-442912679\cdot t^{65}+\frac{1644569069}{2}\cdot t^{63}-1292591872\cdot t^{61}+\frac{55639367641}{32}\cdot t^{59}-\frac{64564422455}{32}\cdot t^{57}+\frac{520258854297}{256}\cdot t^{55}-\frac{228500787123}{128}\cdot t^{53}+\frac{89934700841721}{65536}\cdot t^{51}-\frac{60650453072805}{65536}\cdot t^{49}+\frac{575013464726925}{1048576}\cdot t^{47}-\frac{74901971179455}{262144}\cdot t^{45}+\frac{2196407410747935}{16777216}\cdot t^{43}-\frac{884348069228085}{16777216}\cdot t^{41}+\frac{2499753756530415}{134217728}\cdot t^{39}-\frac{386740267088175}{67108864}\cdot t^{37}+\frac{6687918051923745}{4294967296}\cdot t^{35}-\frac{1572336121450185}{4294967296}\cdot t^{33}+\frac{1280743811157265}{17179869184}\cdot t^{31}-\frac{28082597092459}{2147483648}\cdot t^{29}+\frac{539540996494465}{274877906944}\cdot t^{27}-\frac{68742519953863}{274877906944}\cdot t^{25}+\frac{58902866522353}{2199023255552}\cdot t^{23}-\frac{2620961293159}{1099511627776}\cdot t^{21}+\frac{24454290230667}{140737488355328}\cdot t^{19}-\frac{1434561782775}{140737488355328}\cdot t^{17}+\frac{2119961251221}{4503599627370496}\cdot t^{15}-\frac{18730885957}{1125899906842624}\cdot t^{13}+\frac{31241278523}{72057594037927936}\cdot t^{11}-\frac{570666577}{72057594037927936}\cdot t^9+\frac{54331355}{576460752303423488}\cdot t^7-\frac{187967}{288230376151711744}\cdot t^5+\frac{39559}{18446744073709551616}\cdot t^3-\frac{39}{18446744073709551616}\cdot t$
• $P_4$:
  $4096\cdot t^{157}-161792\cdot t^{155}+3134464\cdot t^{153}-39699968\cdot t^{151}+369708400\cdot t^{149}-2699385320\cdot t^{147}+16091520816\cdot t^{145}-80528165004\cdot t^{143}+\frac{2761944784599}{8}\cdot t^{141}-\frac{20603301212065}{16}\cdot t^{139}+\frac{135335694290797}{32}\cdot t^{137}-\frac{790397673253591}{64}\cdot t^{135}+\frac{132380789541715767}{4096}\cdot t^{133}-\frac{625036894160574693}{8192}\cdot t^{131}+\frac{1338469337421649455}{8192}\cdot t^{129}-\frac{653043702636201627}{2048}\cdot t^{127}+\frac{74636792448239494413}{131072}\cdot t^{125}-\frac{244768449030892449075}{262144}\cdot t^{123}+\frac{739270329089158454925}{524288}\cdot t^{121}-\frac{2061722500999167925875}{1048576}\cdot t^{119}+\frac{85142175265806302253225}{33554432}\cdot t^{117}-\frac{203783965953084491277875}{67108864}\cdot t^{115}+\frac{28317813530572630267775}{8388608}\cdot t^{113}-\frac{468598796298098486266675}{134217728}\cdot t^{111}+\frac{14447280814117395406787625}{4294967296}\cdot t^{109}-\frac{25963278533627351129342415}{8589934592}\cdot t^{107}+\frac{43557900779348494004403135}{17179869184}\cdot t^{105}-\frac{68276392826433828828387365}{34359738368}\cdot t^{103}+\frac{25616181371855569422587592185}{17592186044416}\cdot t^{101}-\frac{35121131721388428630280350875}{35184372088832}\cdot t^{99}+\frac{22534214873641265176501232575}{35184372088832}\cdot t^{97}-\frac{13536866551293857025516632447}{35184372088832}\cdot t^{95}+\frac{974792918776163168966807816909}{4503599627370496}\cdot t^{93}-\frac{1027302951858458766192095583651}{9007199254740992}\cdot t^{91}+\frac{1014093812625461426837756762985}{18014398509481984}\cdot t^{89}-\frac{937630739695072204046529032223}{36028797018963968}\cdot t^{87}+\frac{12990330895277490258715661649199}{1152921504606846976}\cdot t^{85}-\frac{10531838096848587460565742285349}{2305843009213693952}\cdot t^{83}+\frac{1998043572530748985857078103549}{1152921504606846976}\cdot t^{81}-\frac{2837225901713438800866714899535}{4611686018427387904}\cdot t^{79}+\frac{30140609993927778850577841170367}{147573952589676412928}\cdot t^{77}-\frac{18702905533471966841914946922009}{295147905179352825856}\cdot t^{75}+\frac{10838828415554709802380041732685}{590295810358705651712}\cdot t^{73}-\frac{5861721969763271775239564811015}{1180591620717411303424}\cdot t^{71}+\frac{94579126122649653891081087689025}{75557863725914323419136}\cdot t^{69}-\frac{44417306459245083635273340923235}{151115727451828646838272}\cdot t^{67}+\frac{9703420505389864167443267890725}{151115727451828646838272}\cdot t^{65}-\frac{984845808000731121763519406205}{75557863725914323419136}\cdot t^{63}+\frac{11871890086712313643422028711665}{4835703278458516698824704}\cdot t^{61}-\frac{4143386950827949298166148092975}{9671406556917033397649408}\cdot t^{59}+\frac{1337500723943582055512926305801}{19342813113834066795298816}\cdot t^{57}-\frac{398594981628624853114968700359}{38685626227668133590597632}\cdot t^{55}+\frac{1751079912195920196327099226641}{1237940039285380274899124224}\cdot t^{53}-\frac{441983923021608772099619534859}{2475880078570760549798248448}\cdot t^{51}+\frac{12787837790295049540412914725}{618970019642690137449562112}\cdot t^{49}-\frac{10827912704838317609037071415}{4951760157141521099596496896}\cdot t^{47}+\frac{33440038575907144164465358401}{158456325028528675187087900672}\cdot t^{45}-\frac{5866192165014927107647456983}{316912650057057350374175801344}\cdot t^{43}+\frac{931867863965718219533817087}{633825300114114700748351602688}\cdot t^{41}-\frac{133508466371238311820561045}{1267650600228229401496703205376}\cdot t^{39}+\frac{1099129510370005707605927499}{162259276829213363391578010288128}\cdot t^{37}-\frac{126308918604452017859228817}{324518553658426726783156020576256}\cdot t^{35}+\frac{6447120696490495380148881}{324518553658426726783156020576256}\cdot t^{33}-\frac{290476219355370160485087}{324518553658426726783156020576256}\cdot t^{31}+\frac{2936094676557516839553045}{83076749736557242056487941267521536}\cdot t^{29}-\frac{201514215541460679896379}{166153499473114484112975882535043072}\cdot t^{27}+\frac{11906680631100179883273}{332306998946228968225951765070086144}\cdot t^{25}-\frac{598978856504144568015}{664613997892457936451903530140172288}\cdot t^{23}+\frac{405158309707818831435}{21267647932558653966460912964485513216}\cdot t^{21}-\frac{14172290255424418425}{42535295865117307932921825928971026432}\cdot t^{19}+\frac{100633829488392555}{21267647932558653966460912964485513216}\cdot t^{17}-\frac{4535236712336175}{85070591730234615865843651857942052864}\cdot t^{15}+\frac{1259684502303915}{2722258935367507707706996859454145691648}\cdot t^{13}-\frac{16215104845485}{5444517870735015415413993718908291383296}\cdot t^{11}+\frac{146960696025}{10889035741470030830827987437816582766592}\cdot t^9-\frac{870806651}{21778071482940061661655974875633165533184}\cdot t^7+\frac{96239143}{1393796574908163946345982392040522594123776}\cdot t^5-\frac{158197}{2787593149816327892691964784081045188247552}\cdot t^3+\frac{39}{2787593149816327892691964784081045188247552}\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.