Rule: Q[7, 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.

• $P_1$:
  $t^7-21\cdot t^5+105\cdot t^3-105\cdot t$
• $P_2$:
  $t^{49}-\frac{618919329686164932725297736088680388947}{558630557983338258776060990183395474}\cdot t^{47}+\frac{11620898310487819478601791008039259222545971}{20669330645383515574714256636785632538}\cdot t^{45}-\frac{3587290160116009652685329803773707724049981105}{20669330645383515574714256636785632538}\cdot t^{43}+\frac{754566006881577805728427523540030427519838507245}{20669330645383515574714256636785632538}\cdot t^{41}-\frac{114816613173708336043341702255574743274191315236385}{20669330645383515574714256636785632538}\cdot t^{39}+\frac{18629194178896811941898566319552832254487716800635}{29401608314912539935582157378073446}\cdot t^{37}-\frac{1628904071978519555372858005083050705082547523759865}{29401608314912539935582157378073446}\cdot t^{35}+\frac{110740300331398404477414651172723766913523691200217475}{29401608314912539935582157378073446}\cdot t^{33}-\frac{2951833813493762357485027588777914139085574543278666325}{14700804157456269967791078689036723}\cdot t^{31}+\frac{123926379405155783276541004588616332380609220935454716225}{14700804157456269967791078689036723}\cdot t^{29}-\frac{4100404987936772786071693094339729132828850255287673753675}{14700804157456269967791078689036723}\cdot t^{27}+\frac{106676438574128400602765108870839368305867652615239935225575}{14700804157456269967791078689036723}\cdot t^{25}-\frac{2170590164745459752022245188306562066634400861654936590729375}{14700804157456269967791078689036723}\cdot t^{23}+\frac{34252830970270431074637366336815370217731903927319562589076875}{14700804157456269967791078689036723}\cdot t^{21}-\frac{414261137137047896606953011840803981433997619897629608399155625}{14700804157456269967791078689036723}\cdot t^{19}+\frac{3779289276616555652437547525034795855415286866778747360039763750}{14700804157456269967791078689036723}\cdot t^{17}-\frac{50941454074775242556258277913199240311493428989106462453286413125}{29401608314912539935582157378073446}\cdot t^{15}+\frac{246793086183145698452098233639677835733310496062910048243920990625}{29401608314912539935582157378073446}\cdot t^{13}-\frac{828978380270059723260366054488687380665093809254175999868055696875}{29401608314912539935582157378073446}\cdot t^{11}+\frac{1838651888690558583465213589380835405465503511511835490168408059375}{29401608314912539935582157378073446}\cdot t^9-\frac{2513755927208590928536564415160273437259754310352422394836674021875}{29401608314912539935582157378073446}\cdot t^7+\frac{1908191938479753516189023611445309823989673775857708423387268509375}{29401608314912539935582157378073446}\cdot t^5-\frac{669657234834790036467222904613696820504949954794743203675334953125}{29401608314912539935582157378073446}\cdot t^3+\frac{70704837806066127066053658198577652758463853983240899350262546875}{29401608314912539935582157378073446}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.