Rule: Q[1, 4, 20, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{5}{4}\cdot t^3+\frac{5}{16}\cdot t$
• $P_3$:
  $t^{25}-\frac{25}{4}\cdot t^{23}+\frac{275}{16}\cdot t^{21}-\frac{875}{32}\cdot t^{19}+\frac{7125}{256}\cdot t^{17}-\frac{4845}{256}\cdot t^{15}+\frac{8925}{1024}\cdot t^{13}-\frac{5525}{2048}\cdot t^{11}+\frac{17875}{32768}\cdot t^9-\frac{17875}{262144}\cdot t^7+\frac{5005}{1048576}\cdot t^5-\frac{325}{2097152}\cdot t^3+\frac{25}{16777216}\cdot t$
• $P_4$:
  $t^{125}-\frac{125}{4}\cdot t^{123}+\frac{7625}{16}\cdot t^{121}-\frac{75625}{16}\cdot t^{119}+\frac{4388125}{128}\cdot t^{117}-\frac{198518775}{1024}\cdot t^{115}+\frac{3645071625}{4096}\cdot t^{113}-\frac{6981238875}{2048}\cdot t^{111}+\frac{364277464375}{32768}\cdot t^{109}-\frac{4107542443125}{131072}\cdot t^{107}+\frac{40511083817325}{524288}\cdot t^{105}-\frac{88193986300875}{524288}\cdot t^{103}+\frac{1366616548786125}{4194304}\cdot t^{101}-\frac{37919854787746875}{67108864}\cdot t^{99}+\frac{236742877188365625}{268435456}\cdot t^{97}-\frac{83505669408259875}{67108864}\cdot t^{95}+\frac{3420668017503489375}{2147483648}\cdot t^{93}-\frac{15940760107712339375}{8589934592}\cdot t^{91}+\frac{67785475224384246875}{34359738368}\cdot t^{89}-\frac{65900675516059759375}{34359738368}\cdot t^{87}+\frac{469589384963008685375}{274877906944}\cdot t^{85}-\frac{3070392132450441404375}{2199023255552}\cdot t^{83}+\frac{9222016263661828860625}{8796093022208}\cdot t^{81}-\frac{3184072111494493340625}{4398046511104}\cdot t^{79}+\frac{32376654044602422384375}{70368744177664}\cdot t^{77}-\frac{75787271787605350317345}{281474976710656}\cdot t^{75}+\frac{163410784157424123644625}{1125899906842624}\cdot t^{73}-\frac{81149573084979326707875}{1125899906842624}\cdot t^{71}+\frac{296990705620285164755625}{9007199254740992}\cdot t^{69}-\frac{4004253996466603428256875}{288230376151711744}\cdot t^{67}+\frac{6212916200833445740263825}{1152921504606846976}\cdot t^{65}-\frac{277171965033750153134625}{144115188075855872}\cdot t^{63}+\frac{5820611265708753215827125}{9223372036854775808}\cdot t^{61}-\frac{7016942434945334904455625}{36893488147419103232}\cdot t^{59}+\frac{7760819978145745327423125}{147573952589676412928}\cdot t^{57}-\frac{1966074394463588816280525}{147573952589676412928}\cdot t^{55}+\frac{3644969382994293872879625}{1180591620717411303424}\cdot t^{53}-\frac{6170476424774124025587375}{9444732965739290427392}\cdot t^{51}+\frac{4759441888437391489790625}{37778931862957161709568}\cdot t^{49}-\frac{417196158378232885509375}{18889465931478580854784}\cdot t^{47}+\frac{1061150699310281762907375}{302231454903657293676544}\cdot t^{45}-\frac{610069217373506936863125}{1208925819614629174706176}\cdot t^{43}+\frac{316059955988684316688125}{4835703278458516698824704}\cdot t^{41}-\frac{36751157673102827521875}{4835703278458516698824704}\cdot t^{39}+\frac{30564094091772385178125}{38685626227668133590597632}\cdot t^{37}-\frac{45234859255823130063625}{618970019642690137449562112}\cdot t^{35}+\frac{14812735969848520851875}{2475880078570760549798248448}\cdot t^{33}-\frac{266677734318058476875}{618970019642690137449562112}\cdot t^{31}+\frac{536818815835052778125}{19807040628566084398385987584}\cdot t^{29}-\frac{117050719242229553125}{79228162514264337593543950336}\cdot t^{27}+\frac{21911894642145372345}{316912650057057350374175801344}\cdot t^{25}-\frac{870902012803870125}{316912650057057350374175801344}\cdot t^{23}+\frac{232179356416627125}{2535301200456458802993406410752}\cdot t^{21}-\frac{51108663362150625}{20282409603651670423947251286016}\cdot t^{19}+\frac{4558988750614375}{81129638414606681695789005144064}\cdot t^{17}-\frac{40261199356075}{40564819207303340847894502572032}\cdot t^{15}+\frac{8752434642625}{649037107316853453566312041152512}\cdot t^{13}-\frac{352265171375}{2596148429267413814265248164610048}\cdot t^{11}+\frac{9971479375}{10384593717069655257060992658440192}\cdot t^9-\frac{46093125}{10384593717069655257060992658440192}\cdot t^7+\frac{992775}{83076749736557242056487941267521536}\cdot t^5-\frac{81375}{5316911983139663491615228241121378304}\cdot t^3+\frac{125}{21267647932558653966460912964485513216}\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.