Rule: Q[1, 6, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^7-21\cdot t^5+\frac{105}{2}\cdot t^3-\frac{105}{4}\cdot t$
• $P_3$:
  $2\cdot t^{49}-\frac{618919329686164932725297736088680388947}{558630557983338258776060990183395474}\cdot t^{47}+\frac{11620898310487819478601791008039259222545971}{41338661290767031149428513273571265076}\cdot t^{45}-\frac{3587290160116009652685329803773707724049981105}{82677322581534062298857026547142530152}\cdot t^{43}+\frac{754566006881577805728427523540030427519838507245}{165354645163068124597714053094285060304}\cdot t^{41}-\frac{114816613173708336043341702255574743274191315236385}{330709290326136249195428106188570120608}\cdot t^{39}+\frac{18629194178896811941898566319552832254487716800635}{940851466077201277938629036098350272}\cdot t^{37}-\frac{1628904071978519555372858005083050705082547523759865}{1881702932154402555877258072196700544}\cdot t^{35}+\frac{110740300331398404477414651172723766913523691200217475}{3763405864308805111754516144393401088}\cdot t^{33}-\frac{2951833813493762357485027588777914139085574543278666325}{3763405864308805111754516144393401088}\cdot t^{31}+\frac{123926379405155783276541004588616332380609220935454716225}{7526811728617610223509032288786802176}\cdot t^{29}-\frac{4100404987936772786071693094339729132828850255287673753675}{15053623457235220447018064577573604352}\cdot t^{27}+\frac{106676438574128400602765108870839368305867652615239935225575}{30107246914470440894036129155147208704}\cdot t^{25}-\frac{2170590164745459752022245188306562066634400861654936590729375}{60214493828940881788072258310294417408}\cdot t^{23}+\frac{34252830970270431074637366336815370217731903927319562589076875}{120428987657881763576144516620588834816}\cdot t^{21}-\frac{414261137137047896606953011840803981433997619897629608399155625}{240857975315763527152289033241177669632}\cdot t^{19}+\frac{1889644638308277826218773762517397927707643433389373680019881875}{240857975315763527152289033241177669632}\cdot t^{17}-\frac{50941454074775242556258277913199240311493428989106462453286413125}{1926863802526108217218312265929421357056}\cdot t^{15}+\frac{246793086183145698452098233639677835733310496062910048243920990625}{3853727605052216434436624531858842714112}\cdot t^{13}-\frac{828978380270059723260366054488687380665093809254175999868055696875}{7707455210104432868873249063717685428224}\cdot t^{11}+\frac{1838651888690558583465213589380835405465503511511835490168408059375}{15414910420208865737746498127435370856448}\cdot t^9-\frac{2513755927208590928536564415160273437259754310352422394836674021875}{30829820840417731475492996254870741712896}\cdot t^7+\frac{1908191938479753516189023611445309823989673775857708423387268509375}{61659641680835462950985992509741483425792}\cdot t^5-\frac{669657234834790036467222904613696820504949954794743203675334953125}{123319283361670925901971985019482966851584}\cdot t^3+\frac{70704837806066127066053658198577652758463853983240899350262546875}{246638566723341851803943970038965933703168}\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.