Rule: Q[10, 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.

• $P_1$:
  $512\cdot t^{10}-1280\cdot t^8+1120\cdot t^6-400\cdot t^4+50\cdot t^2-1$
• $P_2$:
  $512\cdot t^{50}-6400\cdot t^{48}+37600\cdot t^{46}-138000\cdot t^{44}+354750\cdot t^{42}-678755\cdot t^{40}+\frac{4010825}{4}\cdot t^{38}-\frac{9367475}{8}\cdot t^{36}+\frac{140512125}{128}\cdot t^{34}-\frac{213624125}{256}\cdot t^{32}+\frac{264893915}{512}\cdot t^{30}-\frac{268598725}{1024}\cdot t^{28}+\frac{890616825}{8192}\cdot t^{26}-\frac{601768125}{16384}\cdot t^{24}+\frac{659079375}{65536}\cdot t^{22}-\frac{289994925}{131072}\cdot t^{20}+\frac{1620559875}{4194304}\cdot t^{18}-\frac{441970875}{8388608}\cdot t^{16}+\frac{736618125}{134217728}\cdot t^{14}-\frac{113806875}{268435456}\cdot t^{12}+\frac{50075025}{2147483648}\cdot t^{10}-\frac{3700125}{4294967296}\cdot t^8+\frac{336375}{17179869184}\cdot t^6-\frac{8125}{34359738368}\cdot t^4+\frac{625}{549755813888}\cdot t^2-\frac{1}{1099511627776}$
• $P_3$:
  $512\cdot t^{150}-19200\cdot t^{148}+352800\cdot t^{146}-4234000\cdot t^{144}+37323000\cdot t^{142}-257683140\cdot t^{140}+\frac{11607671075}{8}\cdot t^{138}-\frac{109617696975}{16}\cdot t^{136}+\frac{3543276261375}{128}\cdot t^{134}-\frac{24881114866125}{256}\cdot t^{132}+\frac{614634626092905}{2048}\cdot t^{130}-\frac{3370641818043825}{4096}\cdot t^{128}+\frac{2067978313485825}{1024}\cdot t^{126}-\frac{9143924322684375}{2048}\cdot t^{124}+\frac{292989776826853125}{32768}\cdot t^{122}-\frac{1067929650745186625}{65536}\cdot t^{120}+\frac{28451558605674001875}{1048576}\cdot t^{118}-\frac{86864709887203730625}{2097152}\cdot t^{116}+\frac{975400025164392059375}{16777216}\cdot t^{114}-\frac{2524126782677319909375}{33554432}\cdot t^{112}+\frac{6034604646585469444875}{67108864}\cdot t^{110}-\frac{13354542213466182843125}{134217728}\cdot t^{108}+\frac{3507388404973072930344375}{34359738368}\cdot t^{106}-\frac{6682169282326309776571875}{68719476736}\cdot t^{104}+\frac{47340871264735072967353125}{549755813888}\cdot t^{102}-\frac{78032904923088115473547503}{1099511627776}\cdot t^{100}+\frac{479234341649238426295359975}{8796093022208}\cdot t^{98}-\frac{685877996344122324655780175}{17592186044416}\cdot t^{96}+\frac{457787421447482113646129625}{17592186044416}\cdot t^{94}-\frac{570244747548288492090975375}{35184372088832}\cdot t^{92}+\frac{5304543362749190284206273155}{562949953421312}\cdot t^{90}-\frac{5758930921065466817090301975}{1125899906842624}\cdot t^{88}+\frac{93411811719655114304329135425}{36028797018963968}\cdot t^{86}-\frac{88427912933265848946470600875}{72057594037927936}\cdot t^{84}+\frac{312636617125116378729611069625}{576460752303423488}\cdot t^{82}-\frac{257954336763356892859885307385}{1152921504606846976}\cdot t^{80}+\frac{198619810958140297621159252275}{2305843009213693952}\cdot t^{78}-\frac{142658524828341380951050283325}{4611686018427387904}\cdot t^{76}+\frac{1528484194589371938761253035625}{147573952589676412928}\cdot t^{74}-\frac{953669625683967107090354458125}{295147905179352825856}\cdot t^{72}+\frac{2215981421134745387020859995425}{2361183241434822606848}\cdot t^{70}-\frac{1197492757225421819121811789875}{4722366482869645213696}\cdot t^{68}+\frac{2405545415308210673685614865375}{37778931862957161709568}\cdot t^{66}-\frac{1121472487684440750935806104375}{75557863725914323419136}\cdot t^{64}+\frac{121188279115128245812960179375}{37778931862957161709568}\cdot t^{62}-\frac{48500959959091537107366708825}{75557863725914323419136}\cdot t^{60}+\frac{143556353056173947625483402375}{1208925819614629174706176}\cdot t^{58}-\frac{49018519231947022397216290875}{2417851639229258349412352}\cdot t^{56}+\frac{123347254276467997535478901875}{38685626227668133590597632}\cdot t^{54}-\frac{35665775079738473322544010625}{77371252455336267181195264}\cdot t^{52}+\frac{37834254204586572500554686471}{618970019642690137449562112}\cdot t^{50}-\frac{9179433828603396972307286775}{1237940039285380274899124224}\cdot t^{48}+\frac{2031868398482070601405537575}{2475880078570760549798248448}\cdot t^{46}-\frac{409061231750426584799597625}{4951760157141521099596496896}\cdot t^{44}+\frac{2388715587875947834693946625}{316912650057057350374175801344}\cdot t^{42}-\frac{393623755246160973334256085}{633825300114114700748351602688}\cdot t^{40}+\frac{233302833656539178723951175}{5070602400912917605986812821504}\cdot t^{38}-\frac{30939802312874371371993525}{10141204801825835211973625643008}\cdot t^{36}+\frac{14611750717474403271631125}{81129638414606681695789005144064}\cdot t^{34}-\frac{1526763299032061880310125}{162259276829213363391578010288128}\cdot t^{32}+\frac{70118018177768767836465}{162259276829213363391578010288128}\cdot t^{30}-\frac{5618223965247635661975}{324518553658426726783156020576256}\cdot t^{28}+\frac{3113912989536079589775}{5192296858534827628530496329220096}\cdot t^{26}-\frac{184641802882544401875}{10384593717069655257060992658440192}\cdot t^{24}+\frac{296285683695245668125}{664613997892457936451903530140172288}\cdot t^{22}-\frac{12387691028706198975}{1329227995784915872903807060280344576}\cdot t^{20}+\frac{1698168322838512125}{10633823966279326983230456482242756608}\cdot t^{18}-\frac{46721768278060125}{21267647932558653966460912964485513216}\cdot t^{16}+\frac{1005489991636875}{42535295865117307932921825928971026432}\cdot t^{14}-\frac{16371370413125}{85070591730234615865843651857942052864}\cdot t^{12}+\frac{3087172706475}{2722258935367507707706996859454145691648}\cdot t^{10}-\frac{24767832375}{5444517870735015415413993718908291383296}\cdot t^8+\frac{493945375}{43556142965880123323311949751266331066368}\cdot t^6-\frac{1318125}{87112285931760246646623899502532662132736}\cdot t^4+\frac{5625}{696898287454081973172991196020261297061888}\cdot t^2-\frac{1}{1393796574908163946345982392040522594123776}$

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.