Rule: Q[4, 5, 8, 18]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^9-168\cdot t^7+432\cdot t^5-270\cdot t^3+45\cdot t$
• $P_3$:
  $16\cdot t^{17}-\frac{7832664}{11003}\cdot t^{15}+\frac{652667928}{55015}\cdot t^{13}-\frac{5229229734}{55015}\cdot t^{11}+\frac{107801282178}{275075}\cdot t^9-\frac{454972876533}{550150}\cdot t^7+\frac{461002317867}{550150}\cdot t^5-\frac{157900293621}{440120}\cdot t^3+\frac{44369803107}{880240}\cdot t$
• $P_4$:
  $16\cdot t^{35}-\frac{36890036899075169605030571972955213602296542390122951635364996693759358799981325652117008}{11615349195169249864339020252241967790286614071155670645859947248410514583036436453807}\cdot t^{33}+\frac{5349773236554237678242719479008062357970804649472711680587651761241512524748297321028463084}{19358915325282083107231700420403279650477690118592784409766578747350857638394060756345}\cdot t^{31}-\frac{2969987286618827114640689214129513459352493950185647222025420776323964826290552602261821957786}{212948068578102914179548704624436076155254591304520628507432366220859434022334668319795}\cdot t^{29}+\frac{484859858783784729722036735381749238605173306663164609299911354741665683957780635248902666863639}{1064740342890514570897743523122180380776272956522603142537161831104297170111673341598975}\cdot t^{27}-\frac{1966826001421326146543763277013887878503646153808590188203791605158701169615328568084876820696137}{193589153252820831072317004204032796504776901185927844097665787473508576383940607563450}\cdot t^{25}+\frac{679344208665675067461488098512686296467354970819941658290246094071562642581712352951301726827749761}{4258961371562058283590974092488721523105091826090412570148647324417188680446693366395900}\cdot t^{23}-\frac{609327259271967798440820667946764178863360449399765893656842635822017686491767890019584125831490837}{340716909724964662687277927399097721848407346087233005611891785953375094435735469311672}\cdot t^{21}+\frac{1225075220972547914067455178664035586754131245884640616347468148666848018134420622442149105452070690333}{85179227431241165671819481849774430462101836521808251402972946488343773608933867327918000}\cdot t^{19}-\frac{14078483908471315022170044053866508483779753460892215762733881044109361036702530666900527739033595320343}{170358454862482331343638963699548860924203673043616502805945892976687547217867734655836000}\cdot t^{17}+\frac{114241815754912778470127735766425102961378283441391449282919974790408608222074768410325516669881231707299}{340716909724964662687277927399097721848407346087233005611891785953375094435735469311672000}\cdot t^{15}-\frac{9873815573056117224285258718987195268345579079388596716123625552950884865547147993142236104688813007551}{10483597222306605005762397766126083749181764494991784788058208798565387521099552901897600}\cdot t^{13}+\frac{3394518967459127572896589739891854511517497160978959130214009128123840984095814772445400422954449616307}{1906108585873928182865890502932015227123957180907597234192401599739161367472645982163200}\cdot t^{11}-\frac{8327003471487652011939800015761518235262405973667930602776925124257973165138608137863931965275421809927}{3812217171747856365731781005864030454247914361815194468384803199478322734945291964326400}\cdot t^9+\frac{12622462720716675192626879293623510252506256956924117314511829305133167144754828914915929817494251164037}{7624434343495712731463562011728060908495828723630388936769606398956645469890583928652800}\cdot t^7-\frac{11037162954748057744100226216261469925345729811602134229162966491436372904192636394656248545968119455761}{15248868686991425462927124023456121816991657447260777873539212797913290939781167857305600}\cdot t^5+\frac{249610307466812188902665616211245219538161165270983346479861967963286531628014947859721269464927787191}{1524886868699142546292712402345612181699165744726077787353921279791329093978116785730560}\cdot t^3-\frac{178673726219503798365779220983697533486024342516968460230689457975035601491132623980437401698229039253}{12199094949593140370341699218764897453593325957808622298831370238330632751824934285844480}\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 (physicists') type can be downloaded here packed into a single file.