Rule: Q[1, 12, 52]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-\frac{13}{4}\cdot t^{11}+\frac{65}{16}\cdot t^9-\frac{39}{16}\cdot t^7+\frac{91}{128}\cdot t^5-\frac{91}{1024}\cdot t^3+\frac{13}{4096}\cdot t$
• $P_3$:
  $t^{65}-\frac{65}{4}\cdot t^{63}+\frac{2015}{16}\cdot t^{61}-\frac{19825}{32}\cdot t^{59}+\frac{556075}{256}\cdot t^{57}-\frac{2958319}{512}\cdot t^{55}+\frac{24819795}{2048}\cdot t^{53}-\frac{84240585}{4096}\cdot t^{51}+\frac{1884328875}{65536}\cdot t^{49}-\frac{4396767375}{131072}\cdot t^{47}+\frac{17283292845}{524288}\cdot t^{45}-\frac{28805488075}{1048576}\cdot t^{43}+\frac{163593432275}{8388608}\cdot t^{41}-\frac{198441737375}{16777216}\cdot t^{39}+\frac{411891673375}{67108864}\cdot t^{37}-\frac{365759805957}{134217728}\cdot t^{35}+\frac{4441369072335}{4294967296}\cdot t^{33}-\frac{2873827046805}{8589934592}\cdot t^{31}+\frac{3159171576275}{34359738368}\cdot t^{29}-\frac{1467532791725}{68719476736}\cdot t^{27}+\frac{2289351155091}{549755813888}\cdot t^{25}-\frac{743295829575}{1099511627776}\cdot t^{23}+\frac{397576839075}{4398046511104}\cdot t^{21}-\frac{86429747625}{8796093022208}\cdot t^{19}+\frac{120158429625}{140737488355328}\cdot t^{17}-\frac{16341546429}{281474976710656}\cdot t^{15}+\frac{3384343935}{1125899906842624}\cdot t^{13}-\frac{257289305}{2251799813685248}\cdot t^{11}+\frac{54636725}{18014398509481984}\cdot t^9-\frac{1884025}{36028797018963968}\cdot t^7+\frac{75361}{144115188075855872}\cdot t^5-\frac{715}{288230376151711744}\cdot t^3+\frac{65}{18446744073709551616}\cdot t$

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.