Rule: Q[19, 76]

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.

• $P_1$:
  $262144\cdot t^{19}-1245184\cdot t^{17}+2490368\cdot t^{15}-2723840\cdot t^{13}+1770496\cdot t^{11}-695552\cdot t^9+160512\cdot t^7-20064\cdot t^5+1140\cdot t^3-19\cdot t$
• $P_2$:
  $262144\cdot t^{95}-6225920\cdot t^{93}+71598080\cdot t^{91}-531148800\cdot t^{89}+2857113600\cdot t^{87}-11876068864\cdot t^{85}+39698095360\cdot t^{83}-109653099440\cdot t^{81}+255227041800\cdot t^{79}-507980953350\cdot t^{77}+874324864413\cdot t^{75}-\frac{10503253241325}{8}\cdot t^{73}+\frac{27713403130725}{16}\cdot t^{71}-\frac{129207892645125}{64}\cdot t^{69}+\frac{267303100657375}{128}\cdot t^{67}-\frac{7880095407379415}{4096}\cdot t^{65}+\frac{6483622803540025}{4096}\cdot t^{63}-\frac{19098816493685775}{16384}\cdot t^{61}+\frac{25217052080407625}{32768}\cdot t^{59}-\frac{119519047394951375}{262144}\cdot t^{57}+\frac{127168266428228263}{524288}\cdot t^{55}-\frac{243043597999895715}{2097152}\cdot t^{53}+\frac{208539276490570545}{4194304}\cdot t^{51}-\frac{1284481050847717125}{67108864}\cdot t^{49}+\frac{886472837908987875}{134217728}\cdot t^{47}-\frac{1095173871748132449}{536870912}\cdot t^{45}+\frac{604360163339270415}{1073741824}\cdot t^{43}-\frac{1188969994543270555}{8589934592}\cdot t^{41}+\frac{519699038126589475}{17179869184}\cdot t^{39}-\frac{402400195665415675}{68719476736}\cdot t^{37}+\frac{137435143750341969}{137438953472}\cdot t^{35}-\frac{2637868081659789405}{17592186044416}\cdot t^{33}+\frac{1381740423726556355}{70368744177664}\cdot t^{31}-\frac{628063828966616525}{281474976710656}\cdot t^{29}+\frac{122947885516126475}{562949953421312}\cdot t^{27}-\frac{82199443459353129}{4503599627370496}\cdot t^{25}+\frac{11610090884089425}{9007199254740992}\cdot t^{23}-\frac{2737514439584925}{36028797018963968}\cdot t^{21}+\frac{265409987217375}{72057594037927936}\cdot t^{19}-\frac{166245816169125}{1152921504606846976}\cdot t^{17}+\frac{10277014090455}{2305843009213693952}\cdot t^{15}-\frac{974784534325}{9223372036854775808}\cdot t^{13}+\frac{34156870475}{18446744073709551616}\cdot t^{11}-\frac{3360693875}{147573952589676412928}\cdot t^9+\frac{53914875}{295147905179352825856}\cdot t^7-\frac{1006411}{1180591620717411303424}\cdot t^5+\frac{4465}{2361183241434822606848}\cdot t^3-\frac{95}{75557863725914323419136}\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.