Rule: Q[1, 8, 28, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-\frac{9}{4}\cdot t^7+\frac{27}{16}\cdot t^5-\frac{15}{32}\cdot t^3+\frac{9}{256}\cdot t$
• $P_3$:
  $t^{37}-\frac{19}{2}\cdot t^{35}+\frac{83}{2}\cdot t^{33}-\frac{221}{2}\cdot t^{31}+\frac{51305}{256}\cdot t^{29}-\frac{134183}{512}\cdot t^{27}+\frac{261261}{1024}\cdot t^{25}-\frac{385515}{2048}\cdot t^{23}+\frac{6956235}{65536}\cdot t^{21}-\frac{6002425}{131072}\cdot t^{19}+\frac{985435}{65536}\cdot t^{17}-\frac{973199}{262144}\cdot t^{15}+\frac{5668327}{8388608}\cdot t^{13}-\frac{1476433}{16777216}\cdot t^{11}+\frac{263245}{33554432}\cdot t^9-\frac{30039}{67108864}\cdot t^7+\frac{62985}{4294967296}\cdot t^5-\frac{1947}{8589934592}\cdot t^3+\frac{9}{8589934592}\cdot t$
• $P_4$:
  $t^{109}-\frac{55}{2}\cdot t^{107}+\frac{1471}{4}\cdot t^{105}-\frac{25493}{8}\cdot t^{103}+\frac{5149691}{256}\cdot t^{101}-\frac{50488385}{512}\cdot t^{99}+\frac{200063325}{512}\cdot t^{97}-\frac{658653765}{512}\cdot t^{95}+\frac{58807776489}{16384}\cdot t^{93}-\frac{282308493383}{32768}\cdot t^{91}+\frac{1179445481981}{65536}\cdot t^{89}-\frac{4327949838875}{131072}\cdot t^{87}+\frac{899339136450469}{16777216}\cdot t^{85}-\frac{2599266503688631}{33554432}\cdot t^{83}+\frac{1680052776537643}{16777216}\cdot t^{81}-\frac{7802787084422301}{67108864}\cdot t^{79}+\frac{522528092139354795}{4294967296}\cdot t^{77}-\frac{988142685652281357}{8589934592}\cdot t^{75}+\frac{1692363417154798905}{17179869184}\cdot t^{73}-\frac{2629670686371537435}{34359738368}\cdot t^{71}+\frac{59396525856399840255}{1099511627776}\cdot t^{69}-\frac{76256428625612941725}{2199023255552}\cdot t^{67}+\frac{44549211517664630715}{2199023255552}\cdot t^{65}-\frac{11847385940359593195}{1099511627776}\cdot t^{63}+\frac{183603161167834384665}{35184372088832}\cdot t^{61}-\frac{161897092855891078023}{70368744177664}\cdot t^{59}+\frac{129905564402391940665}{140737488355328}\cdot t^{57}-\frac{94784590929526830983}{281474976710656}\cdot t^{55}+\frac{2010444196944321900883}{18014398509481984}\cdot t^{53}-\frac{1209043727116542626881}{36028797018963968}\cdot t^{51}+\frac{82332668668644666085}{9007199254740992}\cdot t^{49}-\frac{162223182798154013725}{72057594037927936}\cdot t^{47}+\frac{4614034462584949784935}{9223372036854775808}\cdot t^{45}-\frac{1845298511070017840193}{18446744073709551616}\cdot t^{43}+\frac{662170056878683766721}{36893488147419103232}\cdot t^{41}-\frac{212480102294543056827}{73786976294838206464}\cdot t^{39}+\frac{971733618851161846225}{2361183241434822606848}\cdot t^{37}-\frac{246312889996118987587}{4722366482869645213696}\cdot t^{35}+\frac{27543442279667875379}{4722366482869645213696}\cdot t^{33}-\frac{2701681661323424549}{4722366482869645213696}\cdot t^{31}+\frac{7388630078094330989}{151115727451828646838272}\cdot t^{29}-\frac{1091834975350418915}{302231454903657293676544}\cdot t^{27}+\frac{138228178286450889}{604462909807314587353088}\cdot t^{25}-\frac{14834117203420095}{1208925819614629174706176}\cdot t^{23}+\frac{170563151818821195}{309485009821345068724781056}\cdot t^{21}-\frac{12632144873948985}{618970019642690137449562112}\cdot t^{19}+\frac{189316879136175}{309485009821345068724781056}\cdot t^{17}-\frac{17957925924855}{1237940039285380274899124224}\cdot t^{15}+\frac{20947325479395}{79228162514264337593543950336}\cdot t^{13}-\frac{565067974965}{158456325028528675187087900672}\cdot t^{11}+\frac{10714970409}{316912650057057350374175801344}\cdot t^9-\frac{132670395}{633825300114114700748351602688}\cdot t^7+\frac{15305499}{20282409603651670423947251286016}\cdot t^5-\frac{52497}{40564819207303340847894502572032}\cdot t^3+\frac{27}{40564819207303340847894502572032}\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.