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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{17}-\frac{3855458534}{18122395}\cdot t^{15}+\frac{76689404679}{18122395}\cdot t^{13}-\frac{1451963624397}{36244790}\cdot t^{11}+\frac{2765036333631}{14497916}\cdot t^9-\frac{12957851045997}{28995832}\cdot t^7+\frac{27641768331177}{57991664}\cdot t^5-\frac{23638263740091}{115983328}\cdot t^3+\frac{3232373443299}{115983328}\cdot t$
• $P_4$:
  $4\cdot t^{39}-\frac{9446485419007704990201383339770737887657613695569828628943626713697918668452148255942901170149409512117957766791011}{8768681867465767434139771675418440532914477246532267139787342972473711289974498804641625824399249206056982417265}\cdot t^{37}+\frac{716189571033264207916953033495554014258877508698417988532182337511988549034279644752867528375163363304096658690743729117}{5524269576503433483508056155513617535736120665315328298066026072658438112683934246924224269371526999815898922876950}\cdot t^{35}-\frac{102069951680948069387641078243783247625269032229105335768805016395232398419088028001583869799323614654058353009700527409549}{11048539153006866967016112311027235071472241330630656596132052145316876225367868493848448538743053999631797845753900}\cdot t^{33}+\frac{458293070064181253477106519290746354151959123639048232162296226462664703014871003834866016725122528874152470640774604617167}{1052241824095892092096772601050212863949737269583872056774481156696845354796939856556995098927909904726837890071800}\cdot t^{31}-\frac{42364425436955529539791841106159925107641346063665858471150059149783879749602723674648244849924139757746355435580110389995777}{2946277107468497857870963282940596019059264354834841758968547238751166993431431598359586276998147733235146092201040}\cdot t^{29}+\frac{2022654368210633881353461615419858101195404454028430747984339203184393361795572855440849735826320749034229843113610730760922227}{5892554214936995715741926565881192038118528709669683517937094477502333986862863196719172553996295466470292184402080}\cdot t^{27}-\frac{23703263921963121418732886738720926622921887060030198921289661262782921023565295163452552875983104098338084039713450024527054717}{3928369476624663810494617710587461358745685806446455678624729651668222657908575464479448369330863644313528122934720}\cdot t^{25}+\frac{619253379244963340752654331664605077029977801040248396920306295005573445494865397191310544781258015667044136928509030135013474743}{7856738953249327620989235421174922717491371612892911357249459303336445315817150928958896738661727288627056245869440}\cdot t^{23}-\frac{12050771137352058692828834644475786740146946749766190640416589010756266560454059517188190404029099571537522376000060695362223940729}{15713477906498655241978470842349845434982743225785822714498918606672890631634301857917793477323454577254112491738880}\cdot t^{21}+\frac{4974186144288656902893591993104011495078597066932154429091143389835440910653104782647711248049146615675599255305852134777413530477}{897913023228494585255912619562848310570442470044904155114223920381308036093388677595302484418483118700234999527936}\cdot t^{19}-\frac{52876068173775078447018871579012442282019135717664371025076859091027506179724416684249758414001336403157085795713843701627227752809}{1795826046456989170511825239125696621140884940089808310228447840762616072186777355190604968836966237400469999055872}\cdot t^{17}+\frac{31341028618165239236651408051507660608676091997619472847178116591352784732420086007990018934858055548157942208368121067549755799587}{276280930224152180078742344480876403252443836936893586188991975501940934182581131567785379821071728830841538316288}\cdot t^{15}-\frac{2225322207528554564829619605252917013000425489575988966709573344701242217777558831556338027593699833155681869999422043266423316905091}{7183304185827956682047300956502786484563539760359233240913791363050464288747109420762419875347864949601879996223488}\cdot t^{13}+\frac{641620292564118574957628943747404489707768405061583981697561167494338426355036369160482439123255871577406432046046786407154080909341}{1105123720896608720314969377923505613009775347747574344755967902007763736730324526271141519284286915323366153265152}\cdot t^{11}-\frac{1575341027013524018474615444417935917603574887484449028128334788789758696791911802258646118126569503063819161573917130053063860013865}{2210247441793217440629938755847011226019550695495148689511935804015527473460649052542283038568573830646732306530304}\cdot t^9+\frac{2370128724183197868950946193391029507994418628104396964442806842080032815662037996359102831920338541580185931347626606972009661252905}{4420494883586434881259877511694022452039101390990297379023871608031054946921298105084566077137147661293464613060608}\cdot t^7-\frac{997416677519421226948340704502245499290635330613112505123703876746579523141316036159426801457232278281118674012132792287390409304585}{4420494883586434881259877511694022452039101390990297379023871608031054946921298105084566077137147661293464613060608}\cdot t^5+\frac{209349666130210154589211529977287971355905440994913828376497249632286065539012266817237881251697118699472101009015512264346198525605}{4420494883586434881259877511694022452039101390990297379023871608031054946921298105084566077137147661293464613060608}\cdot t^3-\frac{16928220183847446151568826683007215314729340885226934605814405184433285972474237457664531057253317416166854591008750686379273445395}{4420494883586434881259877511694022452039101390990297379023871608031054946921298105084566077137147661293464613060608}\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.