Rule: Q[1, 12, 26, 40]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-\frac{13}{4}\cdot t^{11}+\frac{65}{16}\cdot t^9-\frac{39}{16}\cdot t^7+\frac{91}{128}\cdot t^5-\frac{91}{1024}\cdot t^3+\frac{13}{4096}\cdot t$
• $P_3$:
  $t^{39}-\frac{39}{4}\cdot t^{37}+\frac{351}{8}\cdot t^{35}-\frac{7735}{64}\cdot t^{33}+\frac{7293}{32}\cdot t^{31}-\frac{39897}{128}\cdot t^{29}+\frac{81809}{256}\cdot t^{27}-\frac{4102137}{16384}\cdot t^{25}+\frac{9924525}{65536}\cdot t^{23}-\frac{18599295}{262144}\cdot t^{21}+\frac{13468455}{524288}\cdot t^{19}-\frac{29910465}{4194304}\cdot t^{17}+\frac{6277505}{4194304}\cdot t^{15}-\frac{3900225}{16777216}\cdot t^{13}+\frac{869193}{33554432}\cdot t^{11}-\frac{1062347}{536870912}\cdot t^9+\frac{415701}{4294967296}\cdot t^7-\frac{46683}{17179869184}\cdot t^5+\frac{1235}{34359738368}\cdot t^3-\frac{39}{274877906944}\cdot t$
• $P_4$:
  $t^{79}-20\cdot t^{77}+\frac{3079}{16}\cdot t^{75}-\frac{18981}{16}\cdot t^{73}+\frac{673863}{128}\cdot t^{71}-\frac{1146579}{64}\cdot t^{69}+\frac{199185175}{4096}\cdot t^{67}-\frac{442912679}{4096}\cdot t^{65}+\frac{1644569069}{8192}\cdot t^{63}-\frac{5049187}{16}\cdot t^{61}+\frac{55639367641}{131072}\cdot t^{59}-\frac{64564422455}{131072}\cdot t^{57}+\frac{520258854297}{1048576}\cdot t^{55}-\frac{228500787123}{524288}\cdot t^{53}+\frac{89934700841721}{268435456}\cdot t^{51}-\frac{60650453072805}{268435456}\cdot t^{49}+\frac{575013464726925}{4294967296}\cdot t^{47}-\frac{74901971179455}{1073741824}\cdot t^{45}+\frac{2196407410747935}{68719476736}\cdot t^{43}-\frac{884348069228085}{68719476736}\cdot t^{41}+\frac{2499753756530415}{549755813888}\cdot t^{39}-\frac{386740267088175}{274877906944}\cdot t^{37}+\frac{6687918051923745}{17592186044416}\cdot t^{35}-\frac{1572336121450185}{17592186044416}\cdot t^{33}+\frac{1280743811157265}{70368744177664}\cdot t^{31}-\frac{28082597092459}{8796093022208}\cdot t^{29}+\frac{539540996494465}{1125899906842624}\cdot t^{27}-\frac{68742519953863}{1125899906842624}\cdot t^{25}+\frac{58902866522353}{9007199254740992}\cdot t^{23}-\frac{2620961293159}{4503599627370496}\cdot t^{21}+\frac{24454290230667}{576460752303423488}\cdot t^{19}-\frac{1434561782775}{576460752303423488}\cdot t^{17}+\frac{2119961251221}{18446744073709551616}\cdot t^{15}-\frac{18730885957}{4611686018427387904}\cdot t^{13}+\frac{31241278523}{295147905179352825856}\cdot t^{11}-\frac{570666577}{295147905179352825856}\cdot t^9+\frac{54331355}{2361183241434822606848}\cdot t^7-\frac{187967}{1180591620717411303424}\cdot t^5+\frac{39559}{75557863725914323419136}\cdot t^3-\frac{39}{75557863725914323419136}\cdot t$

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.