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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^9-21\cdot t^7+108\cdot t^5-135\cdot t^3+45\cdot t$
• $P_3$:
  $t^{17}-\frac{979083}{11003}\cdot t^{15}+\frac{163166982}{55015}\cdot t^{13}-\frac{2614614867}{55015}\cdot t^{11}+\frac{107801282178}{275075}\cdot t^9-\frac{454972876533}{275075}\cdot t^7+\frac{922004635734}{275075}\cdot t^5-\frac{157900293621}{55015}\cdot t^3+\frac{44369803107}{55015}\cdot t$
• $P_4$:
  $t^{35}-\frac{4611254612384396200628821496619401700287067798765368954420624586719919849997665706514626}{11615349195169249864339020252241967790286614071155670645859947248410514583036436453807}\cdot t^{33}+\frac{1337443309138559419560679869752015589492701162368177920146912940310378131187074330257115771}{19358915325282083107231700420403279650477690118592784409766578747350857638394060756345}\cdot t^{31}-\frac{1484993643309413557320344607064756729676246975092823611012710388161982413145276301130910978893}{212948068578102914179548704624436076155254591304520628507432366220859434022334668319795}\cdot t^{29}+\frac{484859858783784729722036735381749238605173306663164609299911354741665683957780635248902666863639}{1064740342890514570897743523122180380776272956522603142537161831104297170111673341598975}\cdot t^{27}-\frac{1966826001421326146543763277013887878503646153808590188203791605158701169615328568084876820696137}{96794576626410415536158502102016398252388450592963922048832893736754288191970303781725}\cdot t^{25}+\frac{679344208665675067461488098512686296467354970819941658290246094071562642581712352951301726827749761}{1064740342890514570897743523122180380776272956522603142537161831104297170111673341598975}\cdot t^{23}-\frac{609327259271967798440820667946764178863360449399765893656842635822017686491767890019584125831490837}{42589613715620582835909740924887215231050918260904125701486473244171886804466933663959}\cdot t^{21}+\frac{1225075220972547914067455178664035586754131245884640616347468148666848018134420622442149105452070690333}{5323701714452572854488717615610901903881364782613015712685809155521485850558366707994875}\cdot t^{19}-\frac{14078483908471315022170044053866508483779753460892215762733881044109361036702530666900527739033595320343}{5323701714452572854488717615610901903881364782613015712685809155521485850558366707994875}\cdot t^{17}+\frac{114241815754912778470127735766425102961378283441391449282919974790408608222074768410325516669881231707299}{5323701714452572854488717615610901903881364782613015712685809155521485850558366707994875}\cdot t^{15}-\frac{9873815573056117224285258718987195268345579079388596716123625552950884865547147993142236104688813007551}{81903103299270351607518732547860029290482535117123318656704756238792090008590257046075}\cdot t^{13}+\frac{3394518967459127572896589739891854511517497160978959130214009128123840984095814772445400422954449616307}{7445736663570031964319884777078184480952957737920301696064068748981099091690023367825}\cdot t^{11}-\frac{8327003471487652011939800015761518235262405973667930602776925124257973165138608137863931965275421809927}{7445736663570031964319884777078184480952957737920301696064068748981099091690023367825}\cdot t^9+\frac{12622462720716675192626879293623510252506256956924117314511829305133167144754828914915929817494251164037}{7445736663570031964319884777078184480952957737920301696064068748981099091690023367825}\cdot t^7-\frac{11037162954748057744100226216261469925345729811602134229162966491436372904192636394656248545968119455761}{7445736663570031964319884777078184480952957737920301696064068748981099091690023367825}\cdot t^5+\frac{998441229867248755610662464844980878152644661083933385919447871853146126512059791438885077859711148764}{1489147332714006392863976955415636896190591547584060339212813749796219818338004673565}\cdot t^3-\frac{178673726219503798365779220983697533486024342516968460230689457975035601491132623980437401698229039253}{1489147332714006392863976955415636896190591547584060339212813749796219818338004673565}\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.