Rule: Q[3, 90]

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^{93}-93\cdot t^{91}+\frac{4185}{4}\cdot t^{89}-\frac{30349}{4}\cdot t^{87}+\frac{1275681}{32}\cdot t^{85}-\frac{41401647}{256}\cdot t^{83}+\frac{539807681}{1024}\cdot t^{81}-\frac{726319305}{512}\cdot t^{79}+\frac{26326938573}{8192}\cdot t^{77}-\frac{203790005991}{32768}\cdot t^{75}+\frac{1362692208735}{131072}\cdot t^{73}-\frac{1985119248645}{131072}\cdot t^{71}+\frac{20300499312275}{1048576}\cdot t^{69}-\frac{366345933743055}{16777216}\cdot t^{67}+\frac{1464721264929285}{67108864}\cdot t^{65}-\frac{162746807214365}{8388608}\cdot t^{63}+\frac{4127850837527985}{268435456}\cdot t^{61}-\frac{11693447419003425}{1073741824}\cdot t^{59}+\frac{29640723753947941}{4294967296}\cdot t^{57}-\frac{16823113481970453}{4294967296}\cdot t^{55}+\frac{68444721974592117}{34359738368}\cdot t^{53}-\frac{249515415029068617}{274877906944}\cdot t^{51}+\frac{407339505969350175}{1099511627776}\cdot t^{49}-\frac{74383735872663945}{549755813888}\cdot t^{47}+\frac{388448398446133935}{8796093022208}\cdot t^{45}-\frac{452428134660791289}{35184372088832}\cdot t^{43}+\frac{469050063833173977}{140737488355328}\cdot t^{41}-\frac{107918364854995135}{140737488355328}\cdot t^{39}+\frac{175752765620992077}{1125899906842624}\cdot t^{37}-\frac{2018126584544495229}{72057594037927936}\cdot t^{35}+\frac{1270672293972459959}{288230376151711744}\cdot t^{33}-\frac{43633908117680727}{72057594037927936}\cdot t^{31}+\frac{332619135651172755}{4611686018427387904}\cdot t^{29}-\frac{136407443509470847}{18446744073709551616}\cdot t^{27}+\frac{47735805256056099}{73786976294838206464}\cdot t^{25}-\frac{3527276250447495}{73786976294838206464}\cdot t^{23}+\frac{1739572887647595}{590295810358705651712}\cdot t^{21}-\frac{705232251749025}{4722366482869645213696}\cdot t^{19}+\frac{115401641195295}{18889465931478580854784}\cdot t^{17}-\frac{1863084425755}{9444732965739290427392}\cdot t^{15}+\frac{738203263035}{151115727451828646838272}\cdot t^{13}-\frac{54014872905}{604462909807314587353088}\cdot t^{11}+\frac{2773873025}{2417851639229258349412352}\cdot t^9-\frac{23223123}{2417851639229258349412352}\cdot t^7+\frac{904797}{19342813113834066795298816}\cdot t^5-\frac{33511}{309485009821345068724781056}\cdot t^3+\frac{93}{1237940039285380274899124224}\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.