Rule: Q[2, 8, 40, 100]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{10}-5\cdot t^8+\frac{35}{8}\cdot t^6-\frac{25}{16}\cdot t^4+\frac{25}{128}\cdot t^2-\frac{1}{256}$
• $P_3$:
  $2\cdot t^{50}-25\cdot t^{48}+\frac{1175}{8}\cdot t^{46}-\frac{8625}{16}\cdot t^{44}+\frac{177375}{128}\cdot t^{42}-\frac{678755}{256}\cdot t^{40}+\frac{4010825}{1024}\cdot t^{38}-\frac{9367475}{2048}\cdot t^{36}+\frac{140512125}{32768}\cdot t^{34}-\frac{213624125}{65536}\cdot t^{32}+\frac{264893915}{131072}\cdot t^{30}-\frac{268598725}{262144}\cdot t^{28}+\frac{890616825}{2097152}\cdot t^{26}-\frac{601768125}{4194304}\cdot t^{24}+\frac{659079375}{16777216}\cdot t^{22}-\frac{289994925}{33554432}\cdot t^{20}+\frac{1620559875}{1073741824}\cdot t^{18}-\frac{441970875}{2147483648}\cdot t^{16}+\frac{736618125}{34359738368}\cdot t^{14}-\frac{113806875}{68719476736}\cdot t^{12}+\frac{50075025}{549755813888}\cdot t^{10}-\frac{3700125}{1099511627776}\cdot t^8+\frac{336375}{4398046511104}\cdot t^6-\frac{8125}{8796093022208}\cdot t^4+\frac{625}{140737488355328}\cdot t^2-\frac{1}{281474976710656}$
• $P_4$:
  $2\cdot t^{150}-75\cdot t^{148}+\frac{11025}{8}\cdot t^{146}-\frac{264625}{16}\cdot t^{144}+\frac{4665375}{32}\cdot t^{142}-\frac{64420785}{64}\cdot t^{140}+\frac{11607671075}{2048}\cdot t^{138}-\frac{109617696975}{4096}\cdot t^{136}+\frac{3543276261375}{32768}\cdot t^{134}-\frac{24881114866125}{65536}\cdot t^{132}+\frac{614634626092905}{524288}\cdot t^{130}-\frac{3370641818043825}{1048576}\cdot t^{128}+\frac{2067978313485825}{262144}\cdot t^{126}-\frac{9143924322684375}{524288}\cdot t^{124}+\frac{292989776826853125}{8388608}\cdot t^{122}-\frac{1067929650745186625}{16777216}\cdot t^{120}+\frac{28451558605674001875}{268435456}\cdot t^{118}-\frac{86864709887203730625}{536870912}\cdot t^{116}+\frac{975400025164392059375}{4294967296}\cdot t^{114}-\frac{2524126782677319909375}{8589934592}\cdot t^{112}+\frac{6034604646585469444875}{17179869184}\cdot t^{110}-\frac{13354542213466182843125}{34359738368}\cdot t^{108}+\frac{3507388404973072930344375}{8796093022208}\cdot t^{106}-\frac{6682169282326309776571875}{17592186044416}\cdot t^{104}+\frac{47340871264735072967353125}{140737488355328}\cdot t^{102}-\frac{78032904923088115473547503}{281474976710656}\cdot t^{100}+\frac{479234341649238426295359975}{2251799813685248}\cdot t^{98}-\frac{685877996344122324655780175}{4503599627370496}\cdot t^{96}+\frac{457787421447482113646129625}{4503599627370496}\cdot t^{94}-\frac{570244747548288492090975375}{9007199254740992}\cdot t^{92}+\frac{5304543362749190284206273155}{144115188075855872}\cdot t^{90}-\frac{5758930921065466817090301975}{288230376151711744}\cdot t^{88}+\frac{93411811719655114304329135425}{9223372036854775808}\cdot t^{86}-\frac{88427912933265848946470600875}{18446744073709551616}\cdot t^{84}+\frac{312636617125116378729611069625}{147573952589676412928}\cdot t^{82}-\frac{257954336763356892859885307385}{295147905179352825856}\cdot t^{80}+\frac{198619810958140297621159252275}{590295810358705651712}\cdot t^{78}-\frac{142658524828341380951050283325}{1180591620717411303424}\cdot t^{76}+\frac{1528484194589371938761253035625}{37778931862957161709568}\cdot t^{74}-\frac{953669625683967107090354458125}{75557863725914323419136}\cdot t^{72}+\frac{2215981421134745387020859995425}{604462909807314587353088}\cdot t^{70}-\frac{1197492757225421819121811789875}{1208925819614629174706176}\cdot t^{68}+\frac{2405545415308210673685614865375}{9671406556917033397649408}\cdot t^{66}-\frac{1121472487684440750935806104375}{19342813113834066795298816}\cdot t^{64}+\frac{121188279115128245812960179375}{9671406556917033397649408}\cdot t^{62}-\frac{48500959959091537107366708825}{19342813113834066795298816}\cdot t^{60}+\frac{143556353056173947625483402375}{309485009821345068724781056}\cdot t^{58}-\frac{49018519231947022397216290875}{618970019642690137449562112}\cdot t^{56}+\frac{123347254276467997535478901875}{9903520314283042199192993792}\cdot t^{54}-\frac{35665775079738473322544010625}{19807040628566084398385987584}\cdot t^{52}+\frac{37834254204586572500554686471}{158456325028528675187087900672}\cdot t^{50}-\frac{9179433828603396972307286775}{316912650057057350374175801344}\cdot t^{48}+\frac{2031868398482070601405537575}{633825300114114700748351602688}\cdot t^{46}-\frac{409061231750426584799597625}{1267650600228229401496703205376}\cdot t^{44}+\frac{2388715587875947834693946625}{81129638414606681695789005144064}\cdot t^{42}-\frac{393623755246160973334256085}{162259276829213363391578010288128}\cdot t^{40}+\frac{233302833656539178723951175}{1298074214633706907132624082305024}\cdot t^{38}-\frac{30939802312874371371993525}{2596148429267413814265248164610048}\cdot t^{36}+\frac{14611750717474403271631125}{20769187434139310514121985316880384}\cdot t^{34}-\frac{1526763299032061880310125}{41538374868278621028243970633760768}\cdot t^{32}+\frac{70118018177768767836465}{41538374868278621028243970633760768}\cdot t^{30}-\frac{5618223965247635661975}{83076749736557242056487941267521536}\cdot t^{28}+\frac{3113912989536079589775}{1329227995784915872903807060280344576}\cdot t^{26}-\frac{184641802882544401875}{2658455991569831745807614120560689152}\cdot t^{24}+\frac{296285683695245668125}{170141183460469231731687303715884105728}\cdot t^{22}-\frac{12387691028706198975}{340282366920938463463374607431768211456}\cdot t^{20}+\frac{1698168322838512125}{2722258935367507707706996859454145691648}\cdot t^{18}-\frac{46721768278060125}{5444517870735015415413993718908291383296}\cdot t^{16}+\frac{1005489991636875}{10889035741470030830827987437816582766592}\cdot t^{14}-\frac{16371370413125}{21778071482940061661655974875633165533184}\cdot t^{12}+\frac{3087172706475}{696898287454081973172991196020261297061888}\cdot t^{10}-\frac{24767832375}{1393796574908163946345982392040522594123776}\cdot t^8+\frac{493945375}{11150372599265311570767859136324180752990208}\cdot t^6-\frac{1318125}{22300745198530623141535718272648361505980416}\cdot t^4+\frac{5625}{178405961588244985132285746181186892047843328}\cdot t^2-\frac{1}{356811923176489970264571492362373784095686656}$

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.