Rule: Q[4, 15, 22]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{19}-\frac{748536}{667}\cdot t^{17}+\frac{226304664}{7337}\cdot t^{15}-\frac{3155515020}{7337}\cdot t^{13}+\frac{24226003620}{7337}\cdot t^{11}-\frac{9496214910}{667}\cdot t^9+\frac{1965071745}{58}\cdot t^7-\frac{112008278655}{2668}\cdot t^5+\frac{250467132825}{10672}\cdot t^3-\frac{83438061525}{21344}\cdot t$
• $P_3$:
  $16\cdot t^{41}-\frac{732162665114791791752253947376667905478782925822585029108367615457648376710924}{163457559805901088531342226033401427370951376520220744896767205238813178587}\cdot t^{39}+\frac{263507786995560508558307016963452473324762913701782581696787678449007207629570011958}{469286654202742025173483530941895497982001401989553758598618646240632635723277}\cdot t^{37}-\frac{225494958840358900776734287397376728765848138176297225843747465890679265970686914508}{5394099473594735921534293459102247103241395425167284581593317772880834893371}\cdot t^{35}+\frac{323383255009501980081327789326410666156083975435118099596820013559770247671105183571350}{156428884734247341724494510313965165994000467329851252866206215413544211907759}\cdot t^{33}-\frac{682226906166276488636253913006635816545639685552578247629919561295143931985114868397465}{9480538468742263134817849109937282787515179838172803204012497903851164358046}\cdot t^{31}+\frac{1503051193658546550001899698718711356117530015698239063021920679300253477913559741321715}{824394649455848968245030357385850677175233029406330713392391122074014292004}\cdot t^{29}-\frac{1300538826657401457510873101229717483504590133387998802388914720914895383434368840347653505}{37922153874969052539271396439749131150060719352691212816049991615404657432184}\cdot t^{27}+\frac{36725778838815430088543712696811316215379267146831925489809306156898828977611381718168711695}{75844307749938105078542792879498262300121438705382425632099983230809314864368}\cdot t^{25}-\frac{48876759392480072729871272007788934704892834633470403619012025430228301331839088528767719375}{9480538468742263134817849109937282787515179838172803204012497903851164358046}\cdot t^{23}+\frac{272760665149737615430611836041276464882277757189656327537964042746980484318929366350671604625}{6595157195646791745960242859086805417401864235250645707139128976592114336032}\cdot t^{21}-\frac{6556881556600740928702442739267996011770890793189586987562678284722049345525126824766473614375}{26380628782587166983840971436347221669607456941002582828556515906368457344128}\cdot t^{19}+\frac{58398058658121003568500432283802839076448087207902657835331864436011861032223289056343898309375}{52761257565174333967681942872694443339214913882005165657113031812736914688256}\cdot t^{17}-\frac{378925477926550738125437459628792575665608415061382580312491795301784023884403020317074591130625}{105522515130348667935363885745388886678429827764010331314226063625473829376512}\cdot t^{15}+\frac{1747838337748157610016370956544304929899039075575752672445216150173405648817336528407458688803125}{211045030260697335870727771490777773356859655528020662628452127250947658753024}\cdot t^{13}-\frac{5533942295728277665493992681751419002342864186322740056288225082165856518107746774063969133533125}{422090060521394671741455542981555546713719311056041325256904254501895317506048}\cdot t^{11}+\frac{5716189935110162327316703785586319759719685800963419556886783083699431591257977144852815879500625}{422090060521394671741455542981555546713719311056041325256904254501895317506048}\cdot t^9-\frac{28543465795458005955802612900979454740140648881596524852892939456132389313371574105616583629069375}{3376720484171157373931644343852444373709754488448330602055234036015162540048384}\cdot t^7+\frac{18951588781225363003861505836017108751177662967203375203421956878430809593829633306057105914118125}{6753440968342314747863288687704888747419508976896661204110468072030325080096768}\cdot t^5-\frac{2575476936845141656464107290263634995322968591301152525002254573778780524950415447119987537796875}{6753440968342314747863288687704888747419508976896661204110468072030325080096768}\cdot t^3+\frac{113630886351313560313702913668001205548410336746780884618663576403986952880387544198909303221875}{13506881936684629495726577375409777494839017953793322408220936144060650160193536}\cdot t$

Warning: This rule has negative weights!

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.