Rule: Q[1, 22, 40]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{23}-253\cdot t^{21}+26565\cdot t^{19}-1514205\cdot t^{17}+51482970\cdot t^{15}-1081142370\cdot t^{13}+14054850810\cdot t^{11}-110430970650\cdot t^9+496939367925\cdot t^7-1159525191825\cdot t^5+1159525191825\cdot t^3-316234143225\cdot t$
• $P_3$:
  $t^{63}-\frac{101576178119894402028670598122530462113}{68193586028690041510290950788710897}\cdot t^{61}+\frac{1908278450767544297327510289326949028643137}{1841226822774631120777855671295194219}\cdot t^{59}-\frac{10727602027881127741883004351727170784281204433}{23935948696070204570112123726837524847}\cdot t^{57}+\frac{26965399612705452523011802586316673810771562193677}{199466239133918371417601031056979373725}\cdot t^{55}-\frac{6036619648667560182847948983620382234879275575250981}{199466239133918371417601031056979373725}\cdot t^{53}+\frac{208380889092568679341000092485319884140207298747917243}{39893247826783674283520206211395874745}\cdot t^{51}-\frac{9479187643929794922145583797699495962855326693451887269}{13297749275594558094506735403798624915}\cdot t^{49}+\frac{23129054287045141339555982258356949452319079108524983259}{295505539457656846544594120084413887}\cdot t^{47}-\frac{31027016849414722096581023251168433850338896785081452132117}{4432583091864852698168911801266208305}\cdot t^{45}+\frac{84431468027332244047808845726595999856462992326266748141933}{164169744143142692524774511158007715}\cdot t^{43}-\frac{9227910751418192239078511104683158792809980839286115968235253}{295505539457656846544594120084413887}\cdot t^{41}+\frac{464787530040205749313032148933846630814433278352833746730652347}{295505539457656846544594120084413887}\cdot t^{39}-\frac{498901589749156105242442056211340637063793113836008697550016693}{7577065114298893501143438976523433}\cdot t^{37}+\frac{17365422298110295844929544862038984414519110949941117167860218727}{7577065114298893501143438976523433}\cdot t^{35}-\frac{502054692953474992100359126725820309136201943976286416538947525211}{7577065114298893501143438976523433}\cdot t^{33}+\frac{4009052286121965279938548246331886105318477918062644643511762774185}{2525688371432964500381146325507811}\cdot t^{31}-\frac{8808535840401325290629592355091904004220932959547370085954530925425}{280632041270329388931238480611979}\cdot t^{29}+\frac{429071158380283692904851202177170348182880597474051330174884303556265}{841896123810988166793715441835937}\cdot t^{27}-\frac{1893716925308936145367090963165837151293666398126306883336740443925375}{280632041270329388931238480611979}\cdot t^{25}+\frac{20268431108929061603591301254911552234259884821147553474416596200995825}{280632041270329388931238480611979}\cdot t^{23}-\frac{173443947202974478781259683225826377160540289832552158591097751287183625}{280632041270329388931238480611979}\cdot t^{21}+\frac{1170543430789285315615223118089464006042026344799026321570971900909825875}{280632041270329388931238480611979}\cdot t^{19}-\frac{6124323394678754124607400231337404265109120953816716349369186448913322375}{280632041270329388931238480611979}\cdot t^{17}+\frac{24307580658897131636795402970939372502316826605495970620429045692800184125}{280632041270329388931238480611979}\cdot t^{15}-\frac{71168844974628612351311108469936831385423971620235521036118637908590116125}{280632041270329388931238480611979}\cdot t^{13}+\frac{148131162606660819867922704156823534123270007645899012785803446311995784375}{280632041270329388931238480611979}\cdot t^{11}-\frac{208354537352068978708205876973364687655820538235457879348067394202966241875}{280632041270329388931238480611979}\cdot t^9+\frac{184055051774275561779045286426490164682047939389850504611743521998202288125}{280632041270329388931238480611979}\cdot t^7-\frac{91034982005097905145522440858992727834030191379812125195035188321904053125}{280632041270329388931238480611979}\cdot t^5+\frac{20520763577746853237416445346092614787121339481541213449796871073329984375}{280632041270329388931238480611979}\cdot t^3-\frac{1307886506810393190133249938351352539627413446813812509274544609814596875}{280632041270329388931238480611979}\cdot t$

Warning: This rule has negative weights!

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.