Rule: Q[8, 42]

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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{50}-\frac{16766945183542805182237063185789097259337019017344}{122749103214213163428429988486872850615280185}\cdot t^{48}+\frac{4099367213082069252238778413820796367583217047300736}{122749103214213163428429988486872850615280185}\cdot t^{46}-\frac{121992254138438564955734342519076081016022868812585920}{24549820642842632685685997697374570123056037}\cdot t^{44}+\frac{210380645722731274834764580122430090656228296315669819392}{417346950928324755656661960855367692091952629}\cdot t^{42}-\frac{15448583876841928964284785466397935464888860543538701590752}{417346950928324755656661960855367692091952629}\cdot t^{40}+\frac{851040238556253743826075728060822167497703343342711925312696}{417346950928324755656661960855367692091952629}\cdot t^{38}-\frac{972265978374583068341956810558382191668096775781661371068212}{11279647322387155558288161104199126813296017}\cdot t^{36}+\frac{603632567865176765548011767193611077876796983379604098189925}{212823534384663312420531341588662770062189}\cdot t^{34}-\frac{97262501074086957743856442519329959886267632105279207017411605}{1327017332045547712739783659317544330976002}\cdot t^{32}+\frac{991515611845239828951823564722652515466094640496730561231540865}{663508666022773856369891829658772165488001}\cdot t^{30}-\frac{31939911596126360408618439956797990313943710397248565115157436015}{1327017332045547712739783659317544330976002}\cdot t^{28}+\frac{405721813347607767373944322238274758340117367986023699064561432885}{1327017332045547712739783659317544330976002}\cdot t^{26}-\frac{2023226166698865731114336301377487741558331181463732602104992841875}{663508666022773856369891829658772165488001}\cdot t^{24}+\frac{251649754000317525232455150479802998696012773505734715381610678694875}{10616138656364381701918269274540354647808016}\cdot t^{22}-\frac{3018223810813388403272626082475660181898063933068418065211183884594125}{21232277312728763403836538549080709295616032}\cdot t^{20}+\frac{110164004769635428767904641812725099839702642424260161366629334351995875}{169858218501830107230692308392645674364928256}\cdot t^{18}-\frac{751046361658732995204816423996874505270101364211310885979169523548013875}{339716437003660214461384616785291348729856512}\cdot t^{16}+\frac{1868124668485641163561957324198358869094686035178585892198961481315640625}{339716437003660214461384616785291348729856512}\cdot t^{14}-\frac{6573817254083714368047823941108098106251419584461321072011877886264099375}{679432874007320428922769233570582697459713024}\cdot t^{12}+\frac{3922773484873680253918808850431997636604878388945910438086445336283466875}{339716437003660214461384616785291348729856512}\cdot t^{10}-\frac{11973460391254338646785694322003954817325920096205257407205074961108118125}{1358865748014640857845538467141165394919426048}\cdot t^8+\frac{21377599443097339270014081258542417286966191790923160149235452804765949375}{5435462992058563431382153868564661579677704192}\cdot t^6-\frac{9620973961140072820845284833201637966537637019142853833596012648243265625}{10870925984117126862764307737129323159355408384}\cdot t^4+\frac{3247398975199601167248431400156602164593303084321037179212261548160071875}{43483703936468507451057230948517292637421633536}\cdot t^2-\frac{84159669392864016658268201230066290441059327904791805855537630959409375}{86967407872937014902114461897034585274843267072}$

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.