Rule: Q[1, 78, 80]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{79}-\frac{79}{4}\cdot t^{77}+\frac{1501}{8}\cdot t^{75}-\frac{73075}{64}\cdot t^{73}+\frac{640137}{128}\cdot t^{71}-\frac{8598597}{512}\cdot t^{69}+\frac{46055499}{1024}\cdot t^{67}-\frac{1616328703}{16384}\cdot t^{65}+\frac{1479737545}{8192}\cdot t^{63}-\frac{9174372779}{32768}\cdot t^{61}+\frac{24332032153}{65536}\cdot t^{59}-\frac{222631588309}{524288}\cdot t^{57}+\frac{441940317091}{1048576}\cdot t^{55}-\frac{1529793405315}{4194304}\cdot t^{53}+\frac{2316544299477}{8388608}\cdot t^{51}-\frac{196906265455545}{1073741824}\cdot t^{49}+\frac{459447952729605}{4294967296}\cdot t^{47}-\frac{942434984631315}{17179869184}\cdot t^{45}+\frac{849736461552825}{34359738368}\cdot t^{43}-\frac{2692322893972635}{274877906944}\cdot t^{41}+\frac{1870936248353865}{549755813888}\cdot t^{39}-\frac{2276459376075885}{2199023255552}\cdot t^{37}+\frac{1209028663848915}{4398046511104}\cdot t^{35}-\frac{4468149409876425}{70368744177664}\cdot t^{33}+\frac{893629881975285}{70368744177664}\cdot t^{31}-\frac{615611696471863}{281474976710656}\cdot t^{29}+\frac{181377611587501}{562949953421312}\cdot t^{27}-\frac{181377611587501}{4503599627370496}\cdot t^{25}+\frac{38104540249475}{9007199254740992}\cdot t^{23}-\frac{13297170597403}{36028797018963968}\cdot t^{21}+\frac{1899595799629}{72057594037927936}\cdot t^{19}-\frac{3492805179963}{2305843009213693952}\cdot t^{17}+\frac{1263355065093}{18446744073709551616}\cdot t^{15}-\frac{174772439835}{73786976294838206464}\cdot t^{13}+\frac{8909967521}{147573952589676412928}\cdot t^{11}-\frac{1272852503}{1180591620717411303424}\cdot t^9+\frac{29601221}{2361183241434822606848}\cdot t^7-\frac{800033}{9444732965739290427392}\cdot t^5+\frac{5135}{18889465931478580854784}\cdot t^3-\frac{79}{302231454903657293676544}\cdot t$
• $P_3$:
  $t^{159}-40\cdot t^{157}+\frac{12559}{16}\cdot t^{155}-\frac{161161}{16}\cdot t^{153}+\frac{12167733}{128}\cdot t^{151}-\frac{45028955}{64}\cdot t^{149}+\frac{17419288275}{4096}\cdot t^{147}-\frac{88416033055}{4096}\cdot t^{145}+\frac{3076632858873}{32768}\cdot t^{143}-\frac{2911499347757}{8192}\cdot t^{141}+\frac{621280198191653}{524288}\cdot t^{139}-\frac{1842369703772975}{524288}\cdot t^{137}+\frac{39182987555935171}{4194304}\cdot t^{135}-\frac{47000249382317391}{2097152}\cdot t^{133}+\frac{13096359043777142463}{268435456}\cdot t^{131}-\frac{25992216651792740319}{268435456}\cdot t^{129}+\frac{94443061743891101865}{536870912}\cdot t^{127}-\frac{1231322197573283949}{4194304}\cdot t^{125}+\frac{3877378555628544847275}{8589934592}\cdot t^{123}-\frac{5507317668277288953525}{8589934592}\cdot t^{121}+\frac{57941939613137930797425}{68719476736}\cdot t^{119}-\frac{35347403510014932100875}{34359738368}\cdot t^{117}+\frac{2565223016371616054121525}{2199023255552}\cdot t^{115}-\frac{2707519461086207121093025}{2199023255552}\cdot t^{113}+\frac{21308229663262474462605075}{17592186044416}\cdot t^{111}-\frac{4890088942423987130619505}{4398046511104}\cdot t^{109}+\frac{268352144359906773833352675}{281474976710656}\cdot t^{107}-\frac{215112186118342798995740305}{281474976710656}\cdot t^{105}+\frac{1290570142949349114319585085}{2251799813685248}\cdot t^{103}-\frac{453008823827047143564141805}{1125899906842624}\cdot t^{101}+\frac{305001601611367966462511095225}{1152921504606846976}\cdot t^{99}-\frac{187889852325915016981201892625}{1152921504606846976}\cdot t^{97}+\frac{1735605822975447550887207203525}{18446744073709551616}\cdot t^{95}-\frac{117406992063026574573298034247}{2305843009213693952}\cdot t^{93}+\frac{7623939589856046809247960992851}{295147905179352825856}\cdot t^{91}-\frac{3625730592455843525276094773301}{295147905179352825856}\cdot t^{89}+\frac{12930079680218876441438192445425}{2361183241434822606848}\cdot t^{87}-\frac{2700891562063471810879788606391}{1180591620717411303424}\cdot t^{85}+\frac{67659038457106053909631419815803}{75557863725914323419136}\cdot t^{83}-\frac{24803417604237192748819396927543}{75557863725914323419136}\cdot t^{81}+\frac{68098860412819106502847547457657}{604462909807314587353088}\cdot t^{79}-\frac{5466849908179552811426109196665}{151115727451828646838272}\cdot t^{77}+\frac{105055666307549944725238759912653}{9671406556917033397649408}\cdot t^{75}-\frac{29474841965795011420018681093335}{9671406556917033397649408}\cdot t^{73}+\frac{61765308457641091442537382756555}{77371252455336267181195264}\cdot t^{71}-\frac{7545453748800361941307796767935}{38685626227668133590597632}\cdot t^{69}+\frac{219878511481443775485952650508425}{4951760157141521099596496896}\cdot t^{67}-\frac{46589279604078701154699532550745}{4951760157141521099596496896}\cdot t^{65}+\frac{36703771891437363428760119626005}{19807040628566084398385987584}\cdot t^{63}-\frac{419378030006330563168958300655}{1237940039285380274899124224}\cdot t^{61}+\frac{18190233051319198762388012234679}{316912650057057350374175801344}\cdot t^{59}-\frac{2851475266710117782965599548985}{316912650057057350374175801344}\cdot t^{57}+\frac{3302315486455414704636768313893}{2535301200456458802993406410752}\cdot t^{55}-\frac{220285106225073116382300329151}{1267650600228229401496703205376}\cdot t^{53}+\frac{1729507736068417744251996369549}{81129638414606681695789005144064}\cdot t^{51}-\frac{194611302068168083206218074185}{81129638414606681695789005144064}\cdot t^{49}+\frac{160255315815816343811029991475}{649037107316853453566312041152512}\cdot t^{47}-\frac{3761120007350205541575590805}{162259276829213363391578010288128}\cdot t^{45}+\frac{20541853913729399116401445371}{10384593717069655257060992658440192}\cdot t^{43}-\frac{1587725603204238261168187881}{10384593717069655257060992658440192}\cdot t^{41}+\frac{885599222102045694585360693}{83076749736557242056487941267521536}\cdot t^{39}-\frac{27724206923071634229028125}{41538374868278621028243970633760768}\cdot t^{37}+\frac{397050422903674132040021691}{10633823966279326983230456482242756608}\cdot t^{35}-\frac{19734845490013944539660307}{10633823966279326983230456482242756608}\cdot t^{33}+\frac{27710544376214205309787269}{340282366920938463463374607431768211456}\cdot t^{31}-\frac{133213110579297765906549}{42535295865117307932921825928971026432}\cdot t^{29}+\frac{570015227914163784067035}{5444517870735015415413993718908291383296}\cdot t^{27}-\frac{16406374656822915314493}{5444517870735015415413993718908291383296}\cdot t^{25}+\frac{3216678728733928458585}{43556142965880123323311949751266331066368}\cdot t^{23}-\frac{33127934225397426855}{21778071482940061661655974875633165533184}\cdot t^{21}+\frac{36136671592825016055}{1393796574908163946345982392040522594123776}\cdot t^{19}-\frac{500151864701106675}{1393796574908163946345982392040522594123776}\cdot t^{17}+\frac{43937472603524085}{11150372599265311570767859136324180752990208}\cdot t^{15}-\frac{92930403374865}{2787593149816327892691964784081045188247552}\cdot t^{13}+\frac{37312695085185}{178405961588244985132285746181186892047843328}\cdot t^{11}-\frac{164821998627}{178405961588244985132285746181186892047843328}\cdot t^9+\frac{3808162215}{1427247692705959881058285969449495136382746624}\cdot t^7-\frac{3205267}{713623846352979940529142984724747568191373312}\cdot t^5+\frac{328719}{91343852333181432387730302044767688728495783936}\cdot t^3-\frac{79}{91343852333181432387730302044767688728495783936}\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.