Rule: Q[1, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{81}-3240\cdot t^{79}+2495610\cdot t^{77}-1217025810\cdot t^{75}+\frac{1688623311375}{4}\cdot t^{73}-\frac{221885103114675}{2}\cdot t^{71}+\frac{183794827079989125}{8}\cdot t^{69}-\frac{30798761737832463375}{8}\cdot t^{67}+\frac{68096062202347576522125}{128}\cdot t^{65}-\frac{491804893683621385993125}{8}\cdot t^{63}+\frac{192098991472822513368914625}{32}\cdot t^{61}-\frac{15979143381602963612050625625}{32}\cdot t^{59}+\frac{9113438108640890246739540148125}{256}\cdot t^{57}-\frac{279712446565208862188390501469375}{128}\cdot t^{55}+\frac{59338997592762165764251413526003125}{512}\cdot t^{53}-\frac{2725637956094208814104614927961076875}{512}\cdot t^{51}+\frac{3475188394020116237983384033150373015625}{16384}\cdot t^{49}-\frac{30050158465938652175503379580770872546875}{4096}\cdot t^{47}+\frac{3609357922408853666857683702979257024796875}{16384}\cdot t^{45}-\frac{94033272189072766583923864893406959330234375}{16384}\cdot t^{43}+\frac{16982408957346541645056649999749296855040328125}{131072}\cdot t^{41}-\frac{165780658869335287487457773807076469299203203125}{65536}\cdot t^{39}+\frac{11167588020197949820746019126458514886428143046875}{262144}\cdot t^{37}-\frac{161687252640257273491670624743942845964372679765625}{262144}\cdot t^{35}+\frac{32067971773651025909181340574215331116267248153515625}{4194304}\cdot t^{33}-\frac{42329722741219354200119369557964237073472767562640625}{524288}\cdot t^{31}+\frac{1514101621128230746388885141881028479935756685894453125}{2097152}\cdot t^{29}-\frac{11383801077371512648775691992661065978776244712465703125}{2097152}\cdot t^{27}+\frac{570816311165342991388609698489147736935780270582208828125}{16777216}\cdot t^{25}-\frac{1476249080600024977729163013334002767937362768747091796875}{8388608}\cdot t^{23}+\frac{24899401159453754624365216158233513352543518699534281640625}{33554432}\cdot t^{21}-\frac{84336681346536910824462828923048996839260305272616115234375}{33554432}\cdot t^{19}+\frac{14421572510257811750983143745841378459513512201617355705078125}{2147483648}\cdot t^{17}-\frac{7429294929526751508082225566039497994294839619015001423828125}{536870912}\cdot t^{15}+\frac{45886821623547582844037275554949840552997538823327949970703125}{2147483648}\cdot t^{13}-\frac{51131029809095878026212964189801250901911543260279715681640625}{2147483648}\cdot t^{11}+\frac{312467404388919254604634781159896533289459431035042706943359375}{17179869184}\cdot t^9-\frac{76005584851358737606532784606461318908246888630145523310546875}{8589934592}\cdot t^7+\frac{84006172730449131038799393512404615635430771643845052080078125}{34359738368}\cdot t^5-\frac{10770022144929375774205050450308284055824457903057057958984375}{34359738368}\cdot t^3+\frac{6462013286957625464523030270184970433494674741834234775390625}{549755813888}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.