Rule: Q[3, 74]

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.

• $P_1$:
  $t^3-3\cdot t$
• $P_2$:
  $t^{77}-\frac{16488119093099274189534770977640678783395073}{5745176430208352538466614093945902783016}\cdot t^{75}+\frac{7476706527526620343826255966332986285954465125}{1915058810069450846155538031315300927672}\cdot t^{73}-\frac{1069838064276244650748931331904045160649951512175}{319176468344908474359256338552550154612}\cdot t^{71}+\frac{651117821050250696819646198104458423505779880877125}{319176468344908474359256338552550154612}\cdot t^{69}-\frac{598322661997281125052849247797695417434778297910894525}{638352936689816948718512677105100309224}\cdot t^{67}+\frac{215806998925691078103437512463900558017763520441067089075}{638352936689816948718512677105100309224}\cdot t^{65}-\frac{7842049313628550860353431435675870317830131700930297411250}{79794117086227118589814084638137538653}\cdot t^{63}+\frac{1872050614620436106864643254202325372854491081379841880855250}{79794117086227118589814084638137538653}\cdot t^{61}-\frac{744062115824196242211172057395913421109938512916497128516898125}{159588234172454237179628169276275077306}\cdot t^{59}+\frac{124359526236006929478283290651314305043690233350228332747320339875}{159588234172454237179628169276275077306}\cdot t^{57}-\frac{8807745410426010706141778521925989394627731794370392493700793602625}{79794117086227118589814084638137538653}\cdot t^{55}+\frac{1063479342296685440378801942354508201640634549204997284951878065421875}{79794117086227118589814084638137538653}\cdot t^{53}-\frac{219844040291268235844982464035583145727570505237611601747355979574008125}{159588234172454237179628169276275077306}\cdot t^{51}+\frac{19510274037138566205022508448022389621560090693271344166661793345013421875}{159588234172454237179628169276275077306}\cdot t^{49}-\frac{744762260671835988507177265717923516082884406654199964428223751169843268750}{79794117086227118589814084638137538653}\cdot t^{47}+\frac{48964015199622202281340465530969517317478933252554278735168307792224274525000}{79794117086227118589814084638137538653}\cdot t^{45}-\frac{11090336437877047231358381029741907955014566798289136623510164920488388958359375}{319176468344908474359256338552550154612}\cdot t^{43}+\frac{540542701449921775827991080040041766175263601313494373763056976865279669970890625}{319176468344908474359256338552550154612}\cdot t^{41}-\frac{276168521894567552043598269344577798214366544690956347498256498361083417823203125}{3892395955425713101942150470153050666}\cdot t^{39}+\frac{9923504794113980977784805697652400407266920735986725061241195479683327696266984375}{3892395955425713101942150470153050666}\cdot t^{37}-\frac{609863548329028566235043887020451123638150440011577392395194648088471507772832296875}{7784791910851426203884300940306101332}\cdot t^{35}+\frac{15964752344621925078095620842042511170870247047165367869956314264637832136025201953125}{7784791910851426203884300940306101332}\cdot t^{33}-\frac{88586163106328532137310314158096192944415136939579383774679220529936713093984435468750}{1946197977712856550971075235076525333}\cdot t^{31}+\frac{1657502771614988299136881182168674332269971042359769454859547024586732167701268439843750}{1946197977712856550971075235076525333}\cdot t^{29}-\frac{51924107601297094637922420893987150404336873235613317578270541237664948063829992611765625}{3892395955425713101942150470153050666}\cdot t^{27}+\frac{675169089937281485818365703380332739703358674707647864046490434076163276829757615014984375}{3892395955425713101942150470153050666}\cdot t^{25}-\frac{3607570706983623300137659581621327494156497559636199671035158674688054193321168498728515625}{1946197977712856550971075235076525333}\cdot t^{23}+\frac{31301539729749244893748315821199667663258740680680586594071462751848941843207013941548046875}{1946197977712856550971075235076525333}\cdot t^{21}-\frac{434571122068500527128488523363958034372877032170769482325572466934894671884139905456056640625}{3892395955425713101942150470153050666}\cdot t^{19}+\frac{2370114718718157999760166818902500750959714539520933329331971577267234888008933150610562109375}{3892395955425713101942150470153050666}\cdot t^{17}-\frac{4964381768771570440399372119834515097019162571143763917411491816915444191836202617040932031250}{1946197977712856550971075235076525333}\cdot t^{15}+\frac{15519663531305721218460001424555280161030631578595200736813038978257544948054330989492998046875}{1946197977712856550971075235076525333}\cdot t^{13}-\frac{278908133803325745573344465529812726661196752899089512080080095446395276132944855045331916015625}{15569583821702852407768601880612202664}\cdot t^{11}+\frac{427630724876702410172632050786526722507640764034142281250683822403400989077865583115111552734375}{15569583821702852407768601880612202664}\cdot t^9-\frac{207815928389740556246798831334616898281317235132513895202989667335992846436716022889090708984375}{7784791910851426203884300940306101332}\cdot t^7+\frac{114162698991686592569475687987761697909244545111023526694949465170971357452809018436072361328125}{7784791910851426203884300940306101332}\cdot t^5-\frac{57891589057310555312604715872250561344713893546710242083687364538349669090558751452346923828125}{15569583821702852407768601880612202664}\cdot t^3+\frac{4268969296743775053506191781204781467974261494102604652120645104733531359129090836597919921875}{15569583821702852407768601880612202664}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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