Rule: Q[1, 2, 10, 26]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^{13}-\frac{629}{8}\cdot t^{11}+\frac{17435}{16}\cdot t^9-\frac{105435}{16}\cdot t^7+\frac{557865}{32}\cdot t^5-\frac{2248785}{128}\cdot t^3+\frac{1133055}{256}\cdot t$
• $P_4$:
  $2\cdot t^{39}-\frac{62344019653739501860494948964782623868150229}{107107765571014895711482237366976081467608}\cdot t^{37}+\frac{1233581744529904314609470513581742737711841497885}{16280380366794264148145300079780364383076416}\cdot t^{35}-\frac{190450052906489912692065749584619996195644106830795}{32560760733588528296290600159560728766152832}\cdot t^{33}+\frac{41419600209009034562007305677067523168083740727107195}{138383233117751245259235050678133097256149536}\cdot t^{31}-\frac{175066301769333140233457169580343514664197399121933145}{16280380366794264148145300079780364383076416}\cdot t^{29}+\frac{32656934164920136616048366645889400400865811375206961495}{116533248941264206534092674255269976636757504}\cdot t^{27}-\frac{7967956141139620793661276449581133932940071002880897514625}{1476087819922679949431840540566753037398928384}\cdot t^{25}+\frac{114538386211271892544993287568588998740273341104219398430375}{1476087819922679949431840540566753037398928384}\cdot t^{23}-\frac{2464033845779568995421369434389334031520340661118437410515875}{2952175639845359898863681081133506074797856768}\cdot t^{21}+\frac{1040382453979074178554596810680070099133177055887319055650125}{155377665255018942045456899007026635515676672}\cdot t^{19}-\frac{725689826603055442029691917171482693431296825322208578362375}{18279725324119875534759635177297251237138432}\cdot t^{17}+\frac{3131054153930636782252718342535849163501155239635446349149375}{18279725324119875534759635177297251237138432}\cdot t^{15}-\frac{19212891260161469094091188875725761643023079648839047881258125}{36559450648239751069519270354594502474276864}\cdot t^{13}+\frac{648813938120183219863668890785526731072718353449065117001294375}{584951210371836017112308325673512039588429824}\cdot t^{11}-\frac{1796402629495949352845955540848191923720541892375483071865570625}{1169902420743672034224616651347024079176859648}\cdot t^9+\frac{1519959679967665559326370237295005468949299028008415630493385625}{1169902420743672034224616651347024079176859648}\cdot t^7-\frac{702987496567067711634926914145594171816637244913003162088965625}{1169902420743672034224616651347024079176859648}\cdot t^5+\frac{2331205017591749907313626444424796214669956704613057825904496875}{18718438731898752547593866421552385266829754368}\cdot t^3-\frac{274956935804831972811860612795367023122114018353806821174378125}{37436877463797505095187732843104770533659508736}\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.