Rule: Q[5, 20, 26, 50]

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.

• $P_1$:
  $16\cdot t^5-20\cdot t^3+5\cdot t$
• $P_2$:
  $16\cdot t^{25}-100\cdot t^{23}+275\cdot t^{21}-\frac{875}{2}\cdot t^{19}+\frac{7125}{16}\cdot t^{17}-\frac{4845}{16}\cdot t^{15}+\frac{8925}{64}\cdot t^{13}-\frac{5525}{128}\cdot t^{11}+\frac{17875}{2048}\cdot t^9-\frac{17875}{16384}\cdot t^7+\frac{5005}{65536}\cdot t^5-\frac{325}{131072}\cdot t^3+\frac{25}{1048576}\cdot t$
• $P_3$:
  $16\cdot t^{51}-208\cdot t^{49}+1273\cdot t^{47}-4876\cdot t^{45}+\frac{209715}{16}\cdot t^{43}-\frac{420497}{16}\cdot t^{41}+\frac{5220243}{128}\cdot t^{39}-\frac{3210259}{64}\cdot t^{37}+\frac{203461557}{4096}\cdot t^{35}-\frac{163907965}{4096}\cdot t^{33}+\frac{432375229}{16384}\cdot t^{31}-\frac{29267999}{2048}\cdot t^{29}+\frac{1666443037}{262144}\cdot t^{27}-\frac{607545099}{262144}\cdot t^{25}+\frac{1445389725}{2097152}\cdot t^{23}-\frac{173996955}{1048576}\cdot t^{21}+\frac{4295336595}{134217728}\cdot t^{19}-\frac{654116895}{134217728}\cdot t^{17}+\frac{2469143955}{4294967296}\cdot t^{15}-\frac{54977475}{1073741824}\cdot t^{13}+\frac{228524205}{68719476736}\cdot t^{11}-\frac{10311015}{68719476736}\cdot t^9+\frac{2408445}{549755813888}\cdot t^7-\frac{20345}{274877906944}\cdot t^5+\frac{10425}{17592186044416}\cdot t^3-\frac{25}{17592186044416}\cdot t$
• $P_4$:
  $16\cdot t^{101}-408\cdot t^{99}+5048\cdot t^{97}-40376\cdot t^{95}+\frac{3755065}{16}\cdot t^{93}-\frac{33812599}{32}\cdot t^{91}+\frac{245452389}{64}\cdot t^{89}-\frac{1476192003}{128}\cdot t^{87}+\frac{120029113347}{4096}\cdot t^{85}-\frac{523100058305}{8192}\cdot t^{83}+\frac{494376770041}{4096}\cdot t^{81}-\frac{3271630074147}{16384}\cdot t^{79}+\frac{152695331559459}{524288}\cdot t^{77}-\frac{394958317266261}{1048576}\cdot t^{75}+\frac{910126028842425}{2097152}\cdot t^{73}-\frac{1875557851877835}{4194304}\cdot t^{71}+\frac{110948466413615445}{268435456}\cdot t^{69}-\frac{184431889994883615}{536870912}\cdot t^{67}+\frac{138109040560912905}{536870912}\cdot t^{65}-\frac{46655249572613825}{268435456}\cdot t^{63}+\frac{1821991823291725085}{17179869184}\cdot t^{61}-\frac{2009392504428687235}{34359738368}\cdot t^{59}+\frac{2003139234339385045}{68719476736}\cdot t^{57}-\frac{1804841545270196155}{137438953472}\cdot t^{55}+\frac{23505759086361871725}{4398046511104}\cdot t^{53}-\frac{17271728717926352319}{8796093022208}\cdot t^{51}+\frac{1430423059799094993}{2199023255552}\cdot t^{49}-\frac{3413176438348135739}{17592186044416}\cdot t^{47}+\frac{29277056984424771501}{562949953421312}\cdot t^{45}-\frac{14074072341784425355}{1125899906842624}\cdot t^{43}+\frac{6050645799039207443}{2251799813685248}\cdot t^{41}-\frac{2319093596405381873}{4503599627370496}\cdot t^{39}+\frac{50532528421825268819}{576460752303423488}\cdot t^{37}-\frac{15218433803974624041}{1152921504606846976}\cdot t^{35}+\frac{2017193238916309545}{1152921504606846976}\cdot t^{33}-\frac{234036416267560263}{1152921504606846976}\cdot t^{31}+\frac{6044735182142233619}{295147905179352825856}\cdot t^{29}-\frac{1052626779041855773}{590295810358705651712}\cdot t^{27}+\frac{156790448502127167}{1180591620717411303424}\cdot t^{25}-\frac{19767864500838825}{2361183241434822606848}\cdot t^{23}+\frac{33335144403310365}{75557863725914323419136}\cdot t^{21}-\frac{2893337347330815}{151115727451828646838272}\cdot t^{19}+\frac{50765795571645}{75557863725914323419136}\cdot t^{17}-\frac{5632614911385}{302231454903657293676544}\cdot t^{15}+\frac{3839652247725}{9671406556917033397649408}\cdot t^{13}-\frac{120983049915}{19342813113834066795298816}\cdot t^{11}+\frac{2678236015}{38685626227668133590597632}\cdot t^9-\frac{38698205}{77371252455336267181195264}\cdot t^7+\frac{10416665}{4951760157141521099596496896}\cdot t^5-\frac{41675}{9903520314283042199192993792}\cdot t^3+\frac{25}{9903520314283042199192993792}\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.