Rule: Q[16, 96]

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.

• $P_1$:
  $32768\cdot t^{16}-131072\cdot t^{14}+212992\cdot t^{12}-180224\cdot t^{10}+84480\cdot t^8-21504\cdot t^6+2688\cdot t^4-128\cdot t^2+1$
• $P_2$:
  $32768\cdot t^{112}-917504\cdot t^{110}+12500992\cdot t^{108}-110444544\cdot t^{106}+711370240\cdot t^{104}-3560840192\cdot t^{102}+14419723136\cdot t^{100}-48556210560\cdot t^{98}+138694512495\cdot t^{96}-341125661800\cdot t^{94}+730911895945\cdot t^{92}-1376956434035\cdot t^{90}+\frac{73529473577469}{32}\cdot t^{88}-\frac{54675762403759}{16}\cdot t^{86}+\frac{582623648938015}{128}\cdot t^{84}-\frac{697947092851519}{128}\cdot t^{82}+\frac{772627431786631533}{131072}\cdot t^{80}-\frac{188970796009733409}{32768}\cdot t^{78}+\frac{1341558629827965549}{262144}\cdot t^{76}-\frac{1081902120829004475}{262144}\cdot t^{74}+\frac{25410588072688183365}{8388608}\cdot t^{72}-\frac{8496790046283489885}{4194304}\cdot t^{70}+\frac{41454036286413390045}{33554432}\cdot t^{68}-\frac{23066022144711700665}{33554432}\cdot t^{66}+\frac{1499291439406260543225}{4294967296}\cdot t^{64}-\frac{43427752037974443321}{268435456}\cdot t^{62}+\frac{146908549380697088229}{2147483648}\cdot t^{60}-\frac{56651009238308027487}{2147483648}\cdot t^{58}+\frac{637034818169545370313}{68719476736}\cdot t^{56}-\frac{101893811796956779215}{34359738368}\cdot t^{54}+\frac{237089503547065286271}{274877906944}\cdot t^{52}-\frac{62600693290204812743}{274877906944}\cdot t^{50}+\frac{15337169856100179122035}{281474976710656}\cdot t^{48}-\frac{829513214311517167705}{70368744177664}\cdot t^{46}+\frac{1294941443155988338725}{562949953421312}\cdot t^{44}-\frac{227275436962071422715}{562949953421312}\cdot t^{42}+\frac{1144351761545868391565}{18014398509481984}\cdot t^{40}-\frac{80413907568088049137}{9007199254740992}\cdot t^{38}+\frac{80413907568088049137}{72057594037927936}\cdot t^{36}-\frac{8897218434825337365}{72057594037927936}\cdot t^{34}+\frac{110918656487489205817}{9223372036854775808}\cdot t^{32}-\frac{1181201769533550457}{1152921504606846976}\cdot t^{30}+\frac{699078598295366597}{9223372036854775808}\cdot t^{28}-\frac{44531801509209399}{9223372036854775808}\cdot t^{26}+\frac{77394842195150025}{295147905179352825856}\cdot t^{24}-\frac{1771225244267115}{147573952589676412928}\cdot t^{22}+\frac{539068552603035}{1180591620717411303424}\cdot t^{20}-\frac{16763179213515}{1180591620717411303424}\cdot t^{18}+\frac{854922139889265}{2417851639229258349412352}\cdot t^{16}-\frac{4154140621425}{604462909807314587353088}\cdot t^{14}+\frac{487776511677}{4835703278458516698824704}\cdot t^{12}-\frac{5174099931}{4835703278458516698824704}\cdot t^{10}+\frac{1194023061}{154742504910672534362390528}\cdot t^8-\frac{2672901}{77371252455336267181195264}\cdot t^6+\frac{51205}{618970019642690137449562112}\cdot t^4-\frac{49}{618970019642690137449562112}\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.