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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{59}-\frac{3588231906837371995087661661886888218242921499288}{265026570181444926006858105793526490839484691}\cdot t^{57}+\frac{24042724728529783025348077844128977344454803629453104}{4505451693084563742116587798489950344271239747}\cdot t^{55}-\frac{5870160846137938739484163868701379617832725337035152840}{4505451693084563742116587798489950344271239747}\cdot t^{53}+\frac{76620195192451437700330398377408924777837099422122215655}{346573207160351057085891369114611564943941519}\cdot t^{51}-\frac{1130502035249904081228698011971560994054479066573356417575}{40773318489453065539516631660542537052228414}\cdot t^{49}+\frac{54404297722706330710541480213948347744046072436555002584800}{20386659244726532769758315830271268526114207}\cdot t^{47}-\frac{4118991241893894693693522744304589207148936262080814267882950}{20386659244726532769758315830271268526114207}\cdot t^{45}+\frac{3991542598604251768589313680274933611984411118231481252256899875}{326186547915624524316133053284340296417827312}\cdot t^{43}-\frac{391300492230270233690637013276949052319767671386497733792514227875}{652373095831249048632266106568680592835654624}\cdot t^{41}+\frac{7822524368649155312347657343327273206811031682928244826379099517375}{326186547915624524316133053284340296417827312}\cdot t^{39}-\frac{512807750017557598420166050864341330052712160855127588643347514468625}{652373095831249048632266106568680592835654624}\cdot t^{37}+\frac{110540544890706105553956862536075553578378720819738377482091963873662875}{5218984766649992389058128852549444742685236992}\cdot t^{35}-\frac{4900758311408655449968680492961253914729778420744052478303824473121436875}{10437969533299984778116257705098889485370473984}\cdot t^{33}+\frac{5580216340906399618789598949147640747754662102784565711711778791407911875}{652373095831249048632266106568680592835654624}\cdot t^{31}-\frac{20831147248932609638384371865261653669942411927609928243017375574538170625}{163093273957812262158066526642170148208913656}\cdot t^{29}+\frac{129952577211871604254540128851067387900684996699596822188135488628733663758125}{83503756266399878224930061640791115882963791872}\cdot t^{27}-\frac{2567782615492994974974711404071502466442874408093662755526597293873488178118125}{167007512532799756449860123281582231765927583744}\cdot t^{25}+\frac{10199476741113772536696367323521642601810369351616920028171749617522924959828125}{83503756266399878224930061640791115882963791872}\cdot t^{23}-\frac{128908710528657915381264195481458746144354079628752769038355668078217360191609375}{167007512532799756449860123281582231765927583744}\cdot t^{21}+\frac{5113532039649187421839212308350267742675314571512466890563396329373960395552203125}{1336060100262398051598880986252657854127420669952}\cdot t^{19}-\frac{39104362759487820255867521474183141721319820860824803958704199784655135516098453125}{2672120200524796103197761972505315708254841339904}\cdot t^{17}+\frac{7047965206123837396501307164957080060287270975095282397260722683569919861128265625}{167007512532799756449860123281582231765927583744}\cdot t^{15}-\frac{59576009024700033930117201601018455526957715431677973426428071728439172145375078125}{668030050131199025799440493126328927063710334976}\cdot t^{13}+\frac{2841730910442647288490357702108627809707796787144544926399684050315032983116784140625}{21376961604198368825582095780042525666038730719232}\cdot t^{11}-\frac{5670690586075684355461328693618230971060501202727727526104826677926013579745242140625}{42753923208396737651164191560085051332077461438464}\cdot t^9+\frac{1755741870599283984445280691955705620482541043296858308328439629495783811417797703125}{21376961604198368825582095780042525666038730719232}\cdot t^7-\frac{1199736943445536865426050052248826622557834688131530173985094038249337461206209671875}{42753923208396737651164191560085051332077461438464}\cdot t^5+\frac{1470291696424456278486126902129484563058266893773482172984200597409498121224614765625}{342031385667173901209313532480680410656619691507712}\cdot t^3-\frac{126203755067121776486065876571738567752339819636215213958997203034119699811201015625}{684062771334347802418627064961360821313239383015424}\cdot t$

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.