Rule: Q[4, 55]

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^{59}-\frac{448528988354671499385957707735861027280365187411}{265026570181444926006858105793526490839484691}\cdot t^{57}+\frac{6010681182132445756337019461032244336113700907363276}{4505451693084563742116587798489950344271239747}\cdot t^{55}-\frac{2935080423068969369742081934350689808916362668517576420}{4505451693084563742116587798489950344271239747}\cdot t^{53}+\frac{76620195192451437700330398377408924777837099422122215655}{346573207160351057085891369114611564943941519}\cdot t^{51}-\frac{1130502035249904081228698011971560994054479066573356417575}{20386659244726532769758315830271268526114207}\cdot t^{49}+\frac{217617190890825322842165920855793390976184289746220010339200}{20386659244726532769758315830271268526114207}\cdot t^{47}-\frac{32951929935151157549548181954436713657191490096646514143063600}{20386659244726532769758315830271268526114207}\cdot t^{45}+\frac{3991542598604251768589313680274933611984411118231481252256899875}{20386659244726532769758315830271268526114207}\cdot t^{43}-\frac{391300492230270233690637013276949052319767671386497733792514227875}{20386659244726532769758315830271268526114207}\cdot t^{41}+\frac{31290097474596621249390629373309092827244126731712979305516398069500}{20386659244726532769758315830271268526114207}\cdot t^{39}-\frac{2051231000070230393680664203457365320210848643420510354573390057874500}{20386659244726532769758315830271268526114207}\cdot t^{37}+\frac{110540544890706105553956862536075553578378720819738377482091963873662875}{20386659244726532769758315830271268526114207}\cdot t^{35}-\frac{4900758311408655449968680492961253914729778420744052478303824473121436875}{20386659244726532769758315830271268526114207}\cdot t^{33}+\frac{178566922909004787801267166372724503928149187289106102774776921325053180000}{20386659244726532769758315830271268526114207}\cdot t^{31}-\frac{5332773695726748067426399197506983339505257453468141630212448147081771680000}{20386659244726532769758315830271268526114207}\cdot t^{29}+\frac{129952577211871604254540128851067387900684996699596822188135488628733663758125}{20386659244726532769758315830271268526114207}\cdot t^{27}-\frac{2567782615492994974974711404071502466442874408093662755526597293873488178118125}{20386659244726532769758315830271268526114207}\cdot t^{25}+\frac{40797906964455090146785469294086570407241477406467680112686998470091699839312500}{20386659244726532769758315830271268526114207}\cdot t^{23}-\frac{515634842114631661525056781925834984577416318515011076153422672312869440766437500}{20386659244726532769758315830271268526114207}\cdot t^{21}+\frac{5113532039649187421839212308350267742675314571512466890563396329373960395552203125}{20386659244726532769758315830271268526114207}\cdot t^{19}-\frac{39104362759487820255867521474183141721319820860824803958704199784655135516098453125}{20386659244726532769758315830271268526114207}\cdot t^{17}+\frac{225534886595962796688041829278626561929192671203049036712343125874237435556104500000}{20386659244726532769758315830271268526114207}\cdot t^{15}-\frac{953216144395200542881875225616295288431323446906847574822849147655026754326001250000}{20386659244726532769758315830271268526114207}\cdot t^{13}+\frac{2841730910442647288490357702108627809707796787144544926399684050315032983116784140625}{20386659244726532769758315830271268526114207}\cdot t^{11}-\frac{5670690586075684355461328693618230971060501202727727526104826677926013579745242140625}{20386659244726532769758315830271268526114207}\cdot t^9+\frac{7022967482397135937781122767822822481930164173187433233313758517983135245671190812500}{20386659244726532769758315830271268526114207}\cdot t^7-\frac{4798947773782147461704200208995306490231338752526120695940376152997349844824838687500}{20386659244726532769758315830271268526114207}\cdot t^5+\frac{1470291696424456278486126902129484563058266893773482172984200597409498121224614765625}{20386659244726532769758315830271268526114207}\cdot t^3-\frac{126203755067121776486065876571738567752339819636215213958997203034119699811201015625}{20386659244726532769758315830271268526114207}\cdot t$

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.