Rule: Q[4, 16, 80]

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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^{20}-40\cdot t^{18}+85\cdot t^{16}-100\cdot t^{14}+\frac{2275}{32}\cdot t^{12}-\frac{1001}{32}\cdot t^{10}+\frac{2145}{256}\cdot t^8-\frac{165}{128}\cdot t^6+\frac{825}{8192}\cdot t^4-\frac{25}{8192}\cdot t^2+\frac{1}{65536}$
• $P_3$:
  $8\cdot t^{100}-200\cdot t^{98}+2425\cdot t^{96}-19000\cdot t^{94}+\frac{3460375}{32}\cdot t^{92}-\frac{15247505}{32}\cdot t^{90}+\frac{433094025}{256}\cdot t^{88}-\frac{636668175}{128}\cdot t^{86}+\frac{101174877375}{8192}\cdot t^{84}-\frac{215320892875}{8192}\cdot t^{82}+\frac{3178136378835}{65536}\cdot t^{80}-\frac{1282292001675}{16384}\cdot t^{78}+\frac{116688572152425}{1048576}\cdot t^{76}-\frac{147021410536875}{1048576}\cdot t^{74}+\frac{1319285149036875}{8388608}\cdot t^{72}-\frac{661194674693775}{4194304}\cdot t^{70}+\frac{76037387589784125}{536870912}\cdot t^{68}-\frac{61379577933922125}{536870912}\cdot t^{66}+\frac{356799985550848125}{4294967296}\cdot t^{64}-\frac{14605847361730625}{268435456}\cdot t^{62}+\frac{1104786294441304475}{34359738368}\cdot t^{60}-\frac{589352544050967125}{34359738368}\cdot t^{58}+\frac{2270861900504076125}{274877906944}\cdot t^{56}-\frac{493665630544364375}{137438953472}\cdot t^{54}+\frac{12393605566824305625}{8796093022208}\cdot t^{52}-\frac{4382378928429074469}{8796093022208}\cdot t^{50}+\frac{11160944256394212525}{70368744177664}\cdot t^{48}-\frac{798423713927744275}{17592186044416}\cdot t^{46}+\frac{13116961014527227375}{1125899906842624}\cdot t^{44}-\frac{3013269820238649125}{1125899906842624}\cdot t^{42}+\frac{4941762505191384565}{9007199254740992}\cdot t^{40}-\frac{450511308327405325}{4503599627370496}\cdot t^{38}+\frac{18629967632597996675}{1152921504606846976}\cdot t^{36}-\frac{2654201630153038875}{1152921504606846976}\cdot t^{34}+\frac{2654201630153038875}{9223372036854775808}\cdot t^{32}-\frac{36167143092195255}{1152921504606846976}\cdot t^{30}+\frac{1748078582789437325}{590295810358705651712}\cdot t^{28}-\frac{141736101307251675}{590295810358705651712}\cdot t^{26}+\frac{78207526188211875}{4722366482869645213696}\cdot t^{24}-\frac{2268314126518125}{2361183241434822606848}\cdot t^{22}+\frac{6986407509675825}{151115727451828646838272}\cdot t^{20}-\frac{274373176279125}{151115727451828646838272}\cdot t^{18}+\frac{68931192070125}{1208925819614629174706176}\cdot t^{16}-\frac{421855520625}{302231454903657293676544}\cdot t^{14}+\frac{498556524375}{19342813113834066795298816}\cdot t^{12}-\frac{6647420325}{19342813113834066795298816}\cdot t^{10}+\frac{481697125}{154742504910672534362390528}\cdot t^8-\frac{1353625}{77371252455336267181195264}\cdot t^6+\frac{520625}{9903520314283042199192993792}\cdot t^4-\frac{625}{9903520314283042199192993792}\cdot t^2+\frac{1}{79228162514264337593543950336}$

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.