Rule: Q[6, 7, 60, 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.

• $P_1$:
  $32\cdot t^6-48\cdot t^4+18\cdot t^2-1$
• $P_2$:
  $32\cdot t^{13}-112\cdot t^{11}+152\cdot t^9-100\cdot t^7+\frac{259}{8}\cdot t^5-\frac{73}{16}\cdot t^3+\frac{3}{16}\cdot t$
• $P_3$:
  $32\cdot t^{73}-592\cdot t^{71}+5252\cdot t^{69}-29750\cdot t^{67}+120868\cdot t^{65}-375089\cdot t^{63}+\frac{3698331}{4}\cdot t^{61}-\frac{14868933}{8}\cdot t^{59}+\frac{6357759465}{2048}\cdot t^{57}-\frac{17889085029}{4096}\cdot t^{55}+\frac{85661767653}{16384}\cdot t^{53}-\frac{175852201551}{32768}\cdot t^{51}+\frac{622571894295}{131072}\cdot t^{49}-\frac{954191233275}{262144}\cdot t^{47}+\frac{2539621368165}{1048576}\cdot t^{45}-\frac{2939489267715}{2097152}\cdot t^{43}+\frac{94762249309035}{134217728}\cdot t^{41}-\frac{83075182012935}{268435456}\cdot t^{39}+\frac{126615500395475}{1073741824}\cdot t^{37}-\frac{83707660854545}{2147483648}\cdot t^{35}+\frac{47872084724345}{4294967296}\cdot t^{33}-\frac{23591754285715}{8589934592}\cdot t^{31}+\frac{19938105049961}{34359738368}\cdot t^{29}-\frac{7179915179015}{68719476736}\cdot t^{27}+\frac{69977299992327}{4398046511104}\cdot t^{25}-\frac{17859683486619}{8796093022208}\cdot t^{23}+\frac{7553117124531}{35184372088832}\cdot t^{21}-\frac{1304975313257}{70368744177664}\cdot t^{19}+\frac{362118481075}{281474976710656}\cdot t^{17}-\frac{39478084879}{562949953421312}\cdot t^{15}+\frac{6577149193}{2251799813685248}\cdot t^{13}-\frac{403477711}{4503599627370496}\cdot t^{11}+\frac{1109136457}{576460752303423488}\cdot t^9-\frac{31012845}{1152921504606846976}\cdot t^7+\frac{1007769}{4611686018427387904}\cdot t^5-\frac{7779}{9223372036854775808}\cdot t^3+\frac{9}{9223372036854775808}\cdot t$
• $P_4$:
  $32\cdot t^{145}-1168\cdot t^{143}+20876\cdot t^{141}-243530\cdot t^{139}+\frac{8340973}{4}\cdot t^{137}-\frac{111794329}{8}\cdot t^{135}+\frac{2442228993}{32}\cdot t^{133}-\frac{22352274747}{64}\cdot t^{131}+\frac{174918544515}{128}\cdot t^{129}-\frac{1188468371233}{256}\cdot t^{127}+\frac{14191080350447}{1024}\cdot t^{125}-\frac{75167688345425}{2048}\cdot t^{123}+\frac{1424063351769175}{16384}\cdot t^{121}-\frac{6070292717165875}{32768}\cdot t^{119}+\frac{46830151370907575}{131072}\cdot t^{117}-\frac{164216499602269125}{262144}\cdot t^{115}+\frac{134541987417305992425}{134217728}\cdot t^{113}-\frac{394302927852321081825}{268435456}\cdot t^{111}+\frac{2122564745941508017875}{1073741824}\cdot t^{109}-\frac{5259880985443694793381}{2147483648}\cdot t^{107}+\frac{48106326928760696123121}{17179869184}\cdot t^{105}-\frac{101678411802191689024989}{34359738368}\cdot t^{103}+\frac{397962320027611987273197}{137438953472}\cdot t^{101}-\frac{722068562234582661104175}{274877906944}\cdot t^{99}+\frac{4864469919054055397373195}{2199023255552}\cdot t^{97}-\frac{7612368908452084940515443}{4398046511104}\cdot t^{95}+\frac{22155126263540785944415413}{17592186044416}\cdot t^{93}-\frac{30000167452051888561866907}{35184372088832}\cdot t^{91}+\frac{151279418592969906870475705}{281474976710656}\cdot t^{89}-\frac{177617183310574074858789229}{562949953421312}\cdot t^{87}+\frac{388539215976700743434686129}{2251799813685248}\cdot t^{85}-\frac{395932559406121131719116099}{4503599627370496}\cdot t^{83}+\frac{24057661749535406239427938219}{576460752303423488}\cdot t^{81}-\frac{21277459716743449610709008355}{1152921504606846976}\cdot t^{79}+\frac{35053237529249596462258069617}{4611686018427387904}\cdot t^{77}-\frac{26882284823961824670194577159}{9223372036854775808}\cdot t^{75}+\frac{76739887773672857920441725015}{73786976294838206464}\cdot t^{73}-\frac{50935347548701935399334471035}{147573952589676412928}\cdot t^{71}+\frac{62841197397605871037665437475}{590295810358705651712}\cdot t^{69}-\frac{35997869669443249908004231665}{1180591620717411303424}\cdot t^{67}+\frac{38261364214565438682144676575}{4722366482869645213696}\cdot t^{65}-\frac{18843472719264314319470636595}{9444732965739290427392}\cdot t^{63}+\frac{17179161201535839275013791085}{37778931862957161709568}\cdot t^{61}-\frac{7238047788566153025417148275}{75557863725914323419136}\cdot t^{59}+\frac{11257371476894262037491317277}{604462909807314587353088}\cdot t^{57}-\frac{4032555923427686786034788913}{1208925819614629174706176}\cdot t^{55}+\frac{2656508192933665639120648749}{4835703278458516698824704}\cdot t^{53}-\frac{802876968488744832595746951}{9671406556917033397649408}\cdot t^{51}+\frac{14216244984714833812992623175}{1237940039285380274899124224}\cdot t^{49}-\frac{3591126817458899675478457455}{2475880078570760549798248448}\cdot t^{47}+\frac{1651759360154274382540827597}{9903520314283042199192993792}\cdot t^{45}-\frac{344736323093965921403742171}{19807040628566084398385987584}\cdot t^{43}+\frac{260256635172959705770163751}{158456325028528675187087900672}\cdot t^{41}-\frac{44244224943517592875279035}{316912650057057350374175801344}\cdot t^{39}+\frac{13490458574767998072359451}{1267650600228229401496703205376}\cdot t^{37}-\frac{1835297311146460211871753}{2535301200456458802993406410752}\cdot t^{35}+\frac{886279828155945879878367}{20282409603651670423947251286016}\cdot t^{33}-\frac{94355854847818409986743}{40564819207303340847894502572032}\cdot t^{31}+\frac{17590716440017482412545}{162259276829213363391578010288128}\cdot t^{29}-\frac{1423956723735776351919}{324518553658426726783156020576256}\cdot t^{27}+\frac{396635447247524311437}{2596148429267413814265248164610048}\cdot t^{25}-\frac{23499737452503398385}{5192296858534827628530496329220096}\cdot t^{23}+\frac{2338654894766338005}{20769187434139310514121985316880384}\cdot t^{21}-\frac{96231668617573775}{41538374868278621028243970633760768}\cdot t^{19}+\frac{411350738897288905}{10633823966279326983230456482242756608}\cdot t^{17}-\frac{10893536289348625}{21267647932558653966460912964485513216}\cdot t^{15}+\frac{444332192130715}{85070591730234615865843651857942052864}\cdot t^{13}-\frac{6717303768685}{170141183460469231731687303715884105728}\cdot t^{11}+\frac{285925766725}{1361129467683753853853498429727072845824}\cdot t^9-\frac{1988857041}{2722258935367507707706996859454145691648}\cdot t^7+\frac{16124313}{10889035741470030830827987437816582766592}\cdot t^5-\frac{31107}{21778071482940061661655974875633165533184}\cdot t^3+\frac{9}{21778071482940061661655974875633165533184}\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.