Rule: Q[2, 3, 12, 22]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{17}-\frac{1927729267}{18122395}\cdot t^{15}+\frac{76689404679}{18122395}\cdot t^{13}-\frac{1451963624397}{18122395}\cdot t^{11}+\frac{2765036333631}{3624479}\cdot t^9-\frac{12957851045997}{3624479}\cdot t^7+\frac{27641768331177}{3624479}\cdot t^5-\frac{23638263740091}{3624479}\cdot t^3+\frac{6464746886598}{3624479}\cdot t$
• $P_4$:
  $t^{39}-\frac{9446485419007704990201383339770737887657613695569828628943626713697918668452148255942901170149409512117957766791011}{17537363734931534868279543350836881065828954493064534279574685944947422579948997609283251648798498412113964834530}\cdot t^{37}+\frac{716189571033264207916953033495554014258877508698417988532182337511988549034279644752867528375163363304096658690743729117}{5524269576503433483508056155513617535736120665315328298066026072658438112683934246924224269371526999815898922876950}\cdot t^{35}-\frac{102069951680948069387641078243783247625269032229105335768805016395232398419088028001583869799323614654058353009700527409549}{5524269576503433483508056155513617535736120665315328298066026072658438112683934246924224269371526999815898922876950}\cdot t^{33}+\frac{458293070064181253477106519290746354151959123639048232162296226462664703014871003834866016725122528874152470640774604617167}{263060456023973023024193150262553215987434317395968014193620289174211338699234964139248774731977476181709472517950}\cdot t^{31}-\frac{42364425436955529539791841106159925107641346063665858471150059149783879749602723674648244849924139757746355435580110389995777}{368284638433562232233870410367574502382408044354355219871068404843895874178928949794948284624768466654393261525130}\cdot t^{29}+\frac{2022654368210633881353461615419858101195404454028430747984339203184393361795572855440849735826320749034229843113610730760922227}{368284638433562232233870410367574502382408044354355219871068404843895874178928949794948284624768466654393261525130}\cdot t^{27}-\frac{23703263921963121418732886738720926622921887060030198921289661262782921023565295163452552875983104098338084039713450024527054717}{122761546144520744077956803455858167460802681451451739957022801614631958059642983264982761541589488884797753841710}\cdot t^{25}+\frac{619253379244963340752654331664605077029977801040248396920306295005573445494865397191310544781258015667044136928509030135013474743}{122761546144520744077956803455858167460802681451451739957022801614631958059642983264982761541589488884797753841710}\cdot t^{23}-\frac{12050771137352058692828834644475786740146946749766190640416589010756266560454059517188190404029099571537522376000060695362223940729}{122761546144520744077956803455858167460802681451451739957022801614631958059642983264982761541589488884797753841710}\cdot t^{21}+\frac{4974186144288656902893591993104011495078597066932154429091143389835440910653104782647711248049146615675599255305852134777413530477}{3507472746986306973655908670167376213165790898612906855914937188989484515989799521856650329759699682422792966906}\cdot t^{19}-\frac{52876068173775078447018871579012442282019135717664371025076859091027506179724416684249758414001336403157085795713843701627227752809}{3507472746986306973655908670167376213165790898612906855914937188989484515989799521856650329759699682422792966906}\cdot t^{17}+\frac{31341028618165239236651408051507660608676091997619472847178116591352784732420086007990018934858055548157942208368121067549755799587}{269805595922023613358146820782105862551214684508685142762687476076114193537676886296665409981515360186368689762}\cdot t^{15}-\frac{2225322207528554564829619605252917013000425489575988966709573344701242217777558831556338027593699833155681869999422043266423316905091}{3507472746986306973655908670167376213165790898612906855914937188989484515989799521856650329759699682422792966906}\cdot t^{13}+\frac{641620292564118574957628943747404489707768405061583981697561167494338426355036369160482439123255871577406432046046786407154080909341}{269805595922023613358146820782105862551214684508685142762687476076114193537676886296665409981515360186368689762}\cdot t^{11}-\frac{1575341027013524018474615444417935917603574887484449028128334788789758696791911802258646118126569503063819161573917130053063860013865}{269805595922023613358146820782105862551214684508685142762687476076114193537676886296665409981515360186368689762}\cdot t^9+\frac{2370128724183197868950946193391029507994418628104396964442806842080032815662037996359102831920338541580185931347626606972009661252905}{269805595922023613358146820782105862551214684508685142762687476076114193537676886296665409981515360186368689762}\cdot t^7-\frac{997416677519421226948340704502245499290635330613112505123703876746579523141316036159426801457232278281118674012132792287390409304585}{134902797961011806679073410391052931275607342254342571381343738038057096768838443148332704990757680093184344881}\cdot t^5+\frac{418699332260420309178423059954575942711810881989827656752994499264572131078024533634475762503394237398944202018031024528692397051210}{134902797961011806679073410391052931275607342254342571381343738038057096768838443148332704990757680093184344881}\cdot t^3-\frac{67712880735389784606275306732028861258917363540907738423257620737733143889896949830658124229013269664667418364035002745517093781580}{134902797961011806679073410391052931275607342254342571381343738038057096768838443148332704990757680093184344881}\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.