Rule: Q[3, 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.

• $P_1$:
  $4\cdot t^3-3\cdot t$
• $P_2$:
  $4\cdot t^{103}-104\cdot t^{101}+\frac{5251}{4}\cdot t^{99}-\frac{42875}{4}\cdot t^{97}+\frac{509153}{8}\cdot t^{95}-292904\cdot t^{93}+\frac{1113604041}{1024}\cdot t^{91}-\frac{3428074767}{1024}\cdot t^{89}+\frac{142784912985}{16384}\cdot t^{87}-\frac{159515089019}{8192}\cdot t^{85}+\frac{9901917798773}{262144}\cdot t^{83}-\frac{16828071613993}{262144}\cdot t^{81}+\frac{100949168251359}{1048576}\cdot t^{79}-\frac{33596050443885}{262144}\cdot t^{77}+\frac{5105625125549247}{33554432}\cdot t^{75}-\frac{5427358379144685}{33554432}\cdot t^{73}+\frac{165818311812146745}{1073741824}\cdot t^{71}-\frac{71276785931988945}{536870912}\cdot t^{69}+\frac{1769136551255643975}{17179869184}\cdot t^{67}-\frac{1239953621041274535}{17179869184}\cdot t^{65}+\frac{786161820794773995}{17179869184}\cdot t^{63}-\frac{56403609411757465}{2147483648}\cdot t^{61}+\frac{15010745730447957685}{1099511627776}\cdot t^{59}-\frac{7066173941202386075}{1099511627776}\cdot t^{57}+\frac{48185714866174317915}{17592186044416}\cdot t^{55}-\frac{9291182099349373029}{8796093022208}\cdot t^{53}+\frac{103650202076465032803}{281474976710656}\cdot t^{51}-\frac{32624376467194221047}{281474976710656}\cdot t^{49}+\frac{37025989675974451075}{1125899906842624}\cdot t^{47}-\frac{2362862218616904683}{281474976710656}\cdot t^{45}+\frac{69297357348747843161}{36028797018963968}\cdot t^{43}-\frac{14212524517290784531}{36028797018963968}\cdot t^{41}+\frac{166457690578091734283}{2305843009213693952}\cdot t^{39}-\frac{13539912593912745495}{1152921504606846976}\cdot t^{37}+\frac{62393455234991836137}{36893488147419103232}\cdot t^{35}-\frac{7914070917793461057}{36893488147419103232}\cdot t^{33}+\frac{1758345384699479849}{73786976294838206464}\cdot t^{31}-\frac{10622061845095183}{4611686018427387904}\cdot t^{29}+\frac{3630930791734191155}{18889465931478580854784}\cdot t^{27}-\frac{259302467444214117}{18889465931478580854784}\cdot t^{25}+\frac{250889744011783695}{302231454903657293676544}\cdot t^{23}-\frac{6343755390318885}{151115727451828646838272}\cdot t^{21}+\frac{8456717661537915}{4835703278458516698824704}\cdot t^{19}-\frac{284947026261975}{4835703278458516698824704}\cdot t^{17}+\frac{30364700168565}{19342813113834066795298816}\cdot t^{15}-\frac{155345099595}{4835703278458516698824704}\cdot t^{13}+\frac{300983631585}{618970019642690137449562112}\cdot t^{11}-\frac{3201338595}{618970019642690137449562112}\cdot t^9+\frac{711271925}{19807040628566084398385987584}\cdot t^7-\frac{1437605}{9903520314283042199192993792}\cdot t^5+\frac{88451}{316912650057057350374175801344}\cdot t^3-\frac{51}{316912650057057350374175801344}\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.