Rule: Q[5, 60]

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.

• $P_1$:
  $16\cdot t^5-20\cdot t^3+5\cdot t$
• $P_2$:
  $16\cdot t^{65}-260\cdot t^{63}+2015\cdot t^{61}-\frac{19825}{2}\cdot t^{59}+\frac{556075}{16}\cdot t^{57}-\frac{2958319}{32}\cdot t^{55}+\frac{24819795}{128}\cdot t^{53}-\frac{84240585}{256}\cdot t^{51}+\frac{1884328875}{4096}\cdot t^{49}-\frac{4396767375}{8192}\cdot t^{47}+\frac{17283292845}{32768}\cdot t^{45}-\frac{28805488075}{65536}\cdot t^{43}+\frac{163593432275}{524288}\cdot t^{41}-\frac{198441737375}{1048576}\cdot t^{39}+\frac{411891673375}{4194304}\cdot t^{37}-\frac{365759805957}{8388608}\cdot t^{35}+\frac{4441369072335}{268435456}\cdot t^{33}-\frac{2873827046805}{536870912}\cdot t^{31}+\frac{3159171576275}{2147483648}\cdot t^{29}-\frac{1467532791725}{4294967296}\cdot t^{27}+\frac{2289351155091}{34359738368}\cdot t^{25}-\frac{743295829575}{68719476736}\cdot t^{23}+\frac{397576839075}{274877906944}\cdot t^{21}-\frac{86429747625}{549755813888}\cdot t^{19}+\frac{120158429625}{8796093022208}\cdot t^{17}-\frac{16341546429}{17592186044416}\cdot t^{15}+\frac{3384343935}{70368744177664}\cdot t^{13}-\frac{257289305}{140737488355328}\cdot t^{11}+\frac{54636725}{1125899906842624}\cdot t^9-\frac{1884025}{2251799813685248}\cdot t^7+\frac{75361}{9007199254740992}\cdot t^5-\frac{715}{18014398509481984}\cdot t^3+\frac{65}{1152921504606846976}\cdot t$

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.