Rule: Q[2, 36, 78]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^{38}-37\cdot t^{36}+\frac{315}{2}\cdot t^{34}-\frac{6545}{16}\cdot t^{32}+\frac{5797}{8}\cdot t^{30}-\frac{29667}{32}\cdot t^{28}+\frac{56637}{64}\cdot t^{26}-\frac{2629575}{4096}\cdot t^{24}+\frac{5852925}{16384}\cdot t^{22}-\frac{10015005}{65536}\cdot t^{20}+\frac{6561555}{131072}\cdot t^{18}-\frac{13037895}{1048576}\cdot t^{16}+\frac{2414425}{1048576}\cdot t^{14}-\frac{1300075}{4194304}\cdot t^{12}+\frac{245157}{8388608}\cdot t^{10}-\frac{245157}{134217728}\cdot t^8+\frac{74613}{1073741824}\cdot t^6-\frac{5985}{4294967296}\cdot t^4+\frac{95}{8589934592}\cdot t^2-\frac{1}{68719476736}$
• $P_3$:
  $4\cdot t^{116}-115\cdot t^{114}+\frac{6441}{4}\cdot t^{112}-\frac{29267}{2}\cdot t^{110}+\frac{1552705}{16}\cdot t^{108}-\frac{128164707}{256}\cdot t^{106}+\frac{2141851635}{1024}\cdot t^{104}-\frac{7449193089}{1024}\cdot t^{102}+\frac{352025629371}{16384}\cdot t^{100}-\frac{3585446225075}{65536}\cdot t^{98}+\frac{31853506369685}{262144}\cdot t^{96}-\frac{15571611175575}{65536}\cdot t^{94}+\frac{216074642693455}{524288}\cdot t^{92}-\frac{2676001344126635}{4194304}\cdot t^{90}+\frac{14864612182007175}{16777216}\cdot t^{88}-\frac{18595338376707015}{16777216}\cdot t^{86}+\frac{672930314523407325}{536870912}\cdot t^{84}-\frac{2759805972268938747}{2147483648}\cdot t^{82}+\frac{10286549533002408057}{8589934592}\cdot t^{80}-\frac{4364325526891462065}{4294967296}\cdot t^{78}+\frac{27022823829391877487}{34359738368}\cdot t^{76}-\frac{611230538998149609825}{1099511627776}\cdot t^{74}+\frac{1579840847688040283385}{4398046511104}\cdot t^{72}-\frac{933874469632430842815}{4398046511104}\cdot t^{70}+\frac{8083537075850611058775}{70368744177664}\cdot t^{68}-\frac{16012432572858862601643}{281474976710656}\cdot t^{66}+\frac{29033531588150684937045}{1125899906842624}\cdot t^{64}-\frac{1505442378644850330069}{140737488355328}\cdot t^{62}+\frac{4569488825068077005073}{1125899906842624}\cdot t^{60}-\frac{12677108495878520844795}{9007199254740992}\cdot t^{58}+\frac{16057670761446126403407}{36028797018963968}\cdot t^{56}-\frac{4637811885338903724915}{36028797018963968}\cdot t^{54}+\frac{78078927151999661533569}{2305843009213693952}\cdot t^{52}-\frac{74698887015549459735579}{9223372036854775808}\cdot t^{50}+\frac{64851974907192124859025}{36893488147419103232}\cdot t^{48}-\frac{6372214956037693104615}{18446744073709551616}\cdot t^{46}+\frac{9046971851164626012725}{147573952589676412928}\cdot t^{44}-\frac{23130906408653341102805}{2361183241434822606848}\cdot t^{42}+\frac{13268294748734528107605}{9444732965739290427392}\cdot t^{40}-\frac{1701063429324939500975}{9444732965739290427392}\cdot t^{38}+\frac{3106097638481642777105}{151115727451828646838272}\cdot t^{36}-\frac{1255995835843026283425}{604462909807314587353088}\cdot t^{34}+\frac{447373754862182695239}{2417851639229258349412352}\cdot t^{32}-\frac{8716899057654093999}{604462909807314587353088}\cdot t^{30}+\frac{4722105965229801855}{4835703278458516698824704}\cdot t^{28}-\frac{2203649450440574199}{38685626227668133590597632}\cdot t^{26}+\frac{438570772439183475}{154742504910672534362390528}\cdot t^{24}-\frac{18395977688938395}{154742504910672534362390528}\cdot t^{22}+\frac{20528844667366035}{4951760157141521099596496896}\cdot t^{20}-\frac{2341224781992525}{19807040628566084398385987584}\cdot t^{18}+\frac{213855159190959}{79228162514264337593543950336}\cdot t^{16}-\frac{1906017461595}{39614081257132168796771975168}\cdot t^{14}+\frac{205263418941}{316912650057057350374175801344}\cdot t^{12}-\frac{127805525001}{20282409603651670423947251286016}\cdot t^{10}+\frac{3381098545}{81129638414606681695789005144064}\cdot t^8-\frac{13881343}{81129638414606681695789005144064}\cdot t^6+\frac{487635}{1298074214633706907132624082305024}\cdot t^4-\frac{1711}{5192296858534827628530496329220096}\cdot t^2+\frac{1}{20769187434139310514121985316880384}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.