Rule: Q[16, 68]

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.

• $P_1$:
  $65536\cdot t^{16}-245760\cdot t^{14}+372736\cdot t^{12}-292864\cdot t^{10}+126720\cdot t^8-29568\cdot t^6+3360\cdot t^4-144\cdot t^2+1$
• $P_2$:
  $65536\cdot t^{84}-1359872\cdot t^{82}+13602816\cdot t^{80}-87367680\cdot t^{78}+404884480\cdot t^{76}-1442400960\cdot t^{74}+4109625520\cdot t^{72}-9619233360\cdot t^{70}+18855883575\cdot t^{68}-\frac{125595622175}{4}\cdot t^{66}+\frac{718406958841}{16}\cdot t^{64}-\frac{111203042769}{2}\cdot t^{62}+\frac{960205268841}{16}\cdot t^{60}-\frac{7263091136105}{128}\cdot t^{58}+\frac{24156719613645}{512}\cdot t^{56}-\frac{17714927716673}{512}\cdot t^{54}+\frac{367392196558827}{16384}\cdot t^{52}-\frac{842840921517309}{65536}\cdot t^{50}+\frac{1712239019666175}{262144}\cdot t^{48}-\frac{385048966145025}{131072}\cdot t^{46}+\frac{1226232861415695}{1048576}\cdot t^{44}-\frac{27619435402363035}{67108864}\cdot t^{42}+\frac{34315056105966195}{268435456}\cdot t^{40}-\frac{9384903142585425}{268435456}\cdot t^{38}+\frac{36052387482172425}{4294967296}\cdot t^{36}-\frac{30284005485024837}{17179869184}\cdot t^{34}+\frac{22150361247847371}{68719476736}\cdot t^{32}-\frac{876961939569947}{17179869184}\cdot t^{30}+\frac{956086325095055}{137438953472}\cdot t^{28}-\frac{890149337157465}{1099511627776}\cdot t^{26}+\frac{350664890395365}{4398046511104}\cdot t^{24}-\frac{28907858348005}{4398046511104}\cdot t^{22}+\frac{125994627894135}{281474976710656}\cdot t^{20}-\frac{27900908274925}{1125899906842624}\cdot t^{18}+\frac{4923689695575}{4503599627370496}\cdot t^{16}-\frac{84406109067}{2251799813685248}\cdot t^{14}+\frac{17417133617}{18014398509481984}\cdot t^{12}-\frac{5178066751}{288230376151711744}\cdot t^{10}+\frac{260932815}{1152921504606846976}\cdot t^8-\frac{2036265}{1152921504606846976}\cdot t^6+\frac{135751}{18446744073709551616}\cdot t^4-\frac{903}{73786976294838206464}\cdot t^2+\frac{1}{295147905179352825856}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.