Rule: Q[37, 38]

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.

• $P_1$:
  $68719476736\cdot t^{37}-635655159808\cdot t^{35}+2701534429184\cdot t^{33}-6992206757888\cdot t^{31}+12315818721280\cdot t^{29}-15625695002624\cdot t^{27}+14743599316992\cdot t^{25}-10531142369280\cdot t^{23}+5742196162560\cdot t^{21}-2392581734400\cdot t^{19}+757650882560\cdot t^{17}-180140769280\cdot t^{15}+31524634624\cdot t^{13}-3940579328\cdot t^{11}+336540160\cdot t^9-18356736\cdot t^7+573648\cdot t^5-8436\cdot t^3+37\cdot t$
• $P_2$:
  $68719476736\cdot t^{75}-1305670057984\cdot t^{73}+11909944311808\cdot t^{71}-69449621176320\cdot t^{69}+290839347593216\cdot t^{67}-931614108418048\cdot t^{65}+2373845335932928\cdot t^{63}-4940773611012096\cdot t^{61}+8559042830008320\cdot t^{59}-12512162152972288\cdot t^{57}+15595461872779264\cdot t^{55}-16703380244004864\cdot t^{53}+15462990899785728\cdot t^{51}-12426341692108800\cdot t^{49}+8695289858196480\cdot t^{47}-5308589782487040\cdot t^{45}+2830603295575440\cdot t^{43}-1318425356389680\cdot t^{41}+536069842313775\cdot t^{39}-189992188252230\cdot t^{37}+\frac{936954702926515}{16}\cdot t^{35}-\frac{250352961919515}{16}\cdot t^{33}+\frac{115505564632885}{32}\cdot t^{31}-715187791675\cdot t^{29}+\frac{123844579170319}{1024}\cdot t^{27}-\frac{17736182025705}{1024}\cdot t^{25}+\frac{68191278865263}{32768}\cdot t^{23}-\frac{3397580313853}{16384}\cdot t^{21}+\frac{8860027645865}{524288}\cdot t^{19}-\frac{580273254077}{524288}\cdot t^{17}+\frac{119527914549}{2097152}\cdot t^{15}-\frac{1176468391}{524288}\cdot t^{13}+\frac{17472589069}{268435456}\cdot t^{11}-\frac{355004455}{268435456}\cdot t^9+\frac{75149997}{4294967296}\cdot t^7-\frac{288933}{2147483648}\cdot t^5+\frac{33781}{68719476736}\cdot t^3-\frac{37}{68719476736}\cdot t$

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.