Rule: Q[4, 51]

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^{55}-\frac{18382225325370997463750235915086428596837378}{1638769036930719812305100920195870680311}\cdot t^{53}+\frac{280546374192707494320492583177371059543531973054}{77022144735743831178339743249205921974617}\cdot t^{51}-\frac{112181796988658283776776485689443088587415752906425}{154044289471487662356679486498411843949234}\cdot t^{49}+\frac{7742782489315119499774373269800136236747000019938900}{77022144735743831178339743249205921974617}\cdot t^{47}-\frac{66753623081276346979498684393308292572703540280463675}{6555076147722879249220403680783482721244}\cdot t^{45}+\frac{5149435802153154124352817870923009062153076073528162525}{6555076147722879249220403680783482721244}\cdot t^{43}-\frac{1239317861634305486558009862598510270028767354206265103025}{26220304590891516996881614723133930884976}\cdot t^{41}+\frac{59098483492718788410283375216900301173728071874605425401375}{26220304590891516996881614723133930884976}\cdot t^{39}-\frac{1389248185028250086072551503886305732990700510186338355221375}{16135572055933241228850224445005495929216}\cdot t^{37}+\frac{42800739749777854448495006643825952784858718842794559677549875}{16135572055933241228850224445005495929216}\cdot t^{35}-\frac{4270131765906186371200463111926680140160453693007352810492246625}{64542288223732964915400897780021983716864}\cdot t^{33}+\frac{168622832798092484489394950857907931502233729365703494920892625}{126059156686978447100392378476605436947}\cdot t^{31}-\frac{1413631033966456457988948486478635747755163044887890217439836393125}{64542288223732964915400897780021983716864}\cdot t^{29}+\frac{18687988442114136753568938971310569032982181877658791691942165799375}{64542288223732964915400897780021983716864}\cdot t^{27}-\frac{793726915573986055286015115195341037617289552941320007531656780884375}{258169152894931859661603591120087934867456}\cdot t^{25}+\frac{13437697295601950963405001692595401982146699352404774448768060764915625}{516338305789863719323207182240175869734912}\cdot t^{23}-\frac{718202276273469634647823504759869204105431670913740622583274807368221875}{4130706446318909754585657457921406957879296}\cdot t^{21}+\frac{3737600356108367425899747691375342954047741997467155180264832881148796875}{4130706446318909754585657457921406957879296}\cdot t^{19}-\frac{59590214829042041929899352502861921085538166418723456145633772253982453125}{16522825785275639018342629831685627831517184}\cdot t^{17}+\frac{22249372313045153482381588823993991821870371656526870481383783280269640625}{2065353223159454877292828728960703478939648}\cdot t^{15}-\frac{774529430253434711786246474794175987200607162653277679499770470310783609375}{33045651570551278036685259663371255663034368}\cdot t^{13}+\frac{1181872424829791671862194207455643747992250136977335730597828649049551390625}{33045651570551278036685259663371255663034368}\cdot t^{11}-\frac{4802751632057571412267230153605331327638097998750562536726575593071597578125}{132182606282205112146741038653485022652137472}\cdot t^9+\frac{3013213086442204712942375697497926378490367829195342546933875112375796015625}{132182606282205112146741038653485022652137472}\cdot t^7-\frac{8308517580061238040162375517640377707954179802957298552906554062889165515625}{1057460850257640897173928309227880181217099776}\cdot t^5+\frac{1279865181082955879411807597928359648909161278352742380418686836626903578125}{1057460850257640897173928309227880181217099776}\cdot t^3-\frac{220715386972487411701857022151893591061880873484069933055968924798926234375}{4229843401030563588695713236911520724868399104}\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.