Rule: Q[2, 54]

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^{56}-\frac{8534356927971986410813862099312321}{2845264038326038380917507559814}\cdot t^{54}+\frac{5942442592107288732311488554251426991}{5690528076652076761835015119628}\cdot t^{52}-\frac{196470795276521120381312398399126202421}{875465857946473347974617710712}\cdot t^{50}+\frac{58462678616552042308360469448321815439075}{1750931715892946695949235421424}\cdot t^{48}-\frac{6402096673066718641193685104843586900421875}{1750931715892946695949235421424}\cdot t^{46}+\frac{1071156551687148291975743346645591595832025525}{3501863431785893391898470842848}\cdot t^{44}-\frac{140271721456813155279273558288508367281264088775}{7003726863571786783796941685696}\cdot t^{42}+\frac{14613783788427381554149440380477957693814241854075}{14007453727143573567593883371392}\cdot t^{40}-\frac{2449342749544642860370291102026901742223622266648375}{56029814908574294270375533485568}\cdot t^{38}+\frac{166303763862726332803567281428731644471616815618239625}{112059629817148588540751066971136}\cdot t^{36}-\frac{9187618312041135608141359271139310979354107373762913375}{224119259634297177081502133942272}\cdot t^{34}+\frac{413763984433396423279665695826096598496855015628995804625}{448238519268594354163004267884544}\cdot t^{32}-\frac{3796372675736911527150894836159797744608021802329796208625}{224119259634297177081502133942272}\cdot t^{30}+\frac{113288712320038825826216774528064076750529489238032755044375}{448238519268594354163004267884544}\cdot t^{28}-\frac{2737191295827955095882174779501307834198605186372620422883125}{896477038537188708326008535769088}\cdot t^{26}+\frac{13302184193547700450104659738921957869410263348167422047821875}{448238519268594354163004267884544}\cdot t^{24}-\frac{3300198587557141020598034434343641395336924975682862267247571875}{14343632616595019333216136572305408}\cdot t^{22}+\frac{40360309867884152083094769497711196026870185485624201587148778125}{28687265233190038666432273144610816}\cdot t^{20}-\frac{383680711954516610685147637546789941469165004499850040779537171875}{57374530466380077332864546289221632}\cdot t^{18}+\frac{2782751188010966509126008987890979608422655379197454202510037203125}{114749060932760154665729092578443264}\cdot t^{16}-\frac{7515271227342516990030395852997189041731995639917301694447471546875}{114749060932760154665729092578443264}\cdot t^{14}+\frac{29284729749703945446034986745174259427515127630618673442583188578125}{229498121865520309331458185156886528}\cdot t^{12}-\frac{78865881821583202634709573151946505914746175545401805732035702609375}{458996243731040618662916370313773056}\cdot t^{10}+\frac{138182478286334259925950916288698762217037417239210648081235207109375}{917992487462081237325832740627546112}\cdot t^8-\frac{287820799072128033402479897735195129890393691940976119329383776890625}{3671969949848324949303330962510184448}\cdot t^6+\frac{153526642374731148790863313259829826393052059191992530936615782609375}{7343939899696649898606661925020368896}\cdot t^4-\frac{31333960832513668684510203619514735248570954691187776228745846515625}{14687879799393299797213323850040737792}\cdot t^2+\frac{1019674643792792614045464439014307863841956611338868691445212984375}{29375759598786599594426647700081475584}$

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.