Rule: Q[10, 50]

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.

• $P_1$:
  $t^{10}-45\cdot t^8+630\cdot t^6-3150\cdot t^4+4725\cdot t^2-945$
• $P_2$:
  $t^{60}-\frac{9492312571058968951805187175243884534893418794829241417956725055}{6220146751176593171680212982440348523387779739533737982683084}\cdot t^{58}+\frac{289569461652281171936368882336014833847419423922444965975131802095485}{267466310300593506382249158244934986505674528799950733255372612}\cdot t^{56}-\frac{444476881040471483842610519247339325614352858571271815305505070928268175}{936132086052077272337872053857272452769860850799827566393804142}\cdot t^{54}+\frac{5542177081294463781808169967133566159293093638895968631678234400373949523825}{38381415528135168165852754208148170563564294882792930222145969822}\cdot t^{52}-\frac{355109331476178551419205594774450558644348835627276455506956230103934755580315}{10966118722324333761672215488042334446732655680797980063470277092}\cdot t^{50}+\frac{60966443099370377729126837729178350892445784833233454398642990970612320756040875}{10966118722324333761672215488042334446732655680797980063470277092}\cdot t^{48}-\frac{2053059687514629304920361645665789629893168791122074029185885163909787252989209625}{2741529680581083440418053872010583611683163920199495015867569273}\cdot t^{46}+\frac{220629333209978380816381282002344461923997129458666359405736409363415056634544986250}{2741529680581083440418053872010583611683163920199495015867569273}\cdot t^{44}-\frac{161806840260447656030313538886419870869025034425079452090135602086207837078037763125}{23184183345294574548989884752732208132627179029171205208182404}\cdot t^{42}+\frac{278347227111725076345589360732686897076634993163499849612007620598253322625627989125}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{40}-\frac{8022505071050841186752934233240525043231844333859878143026519027205289755014565624375}{282733943235299689621827862838197660153989988160624453758322}\cdot t^{38}+\frac{378963633366278168606792729676396804029606790710339744988421399727883563088238058488125}{282733943235299689621827862838197660153989988160624453758322}\cdot t^{36}-\frac{29360840282070420475070114379777809346899341524712047615322268367381755806428189366121875}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{34}+\frac{931820708516374283770996874732518598346194617807415403178109133981549769266677454869221875}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{32}-\frac{6041163634059030193955074599741601341922267353095875241959975115822938332517430125685148750}{141366971617649844810913931419098830076994994080312226879161}\cdot t^{30}+\frac{127470764937521247835001761339776314630236345009719362595319040793633515967255190163557940625}{141366971617649844810913931419098830076994994080312226879161}\cdot t^{28}-\frac{8702112542181446307115650910398999491918983261784683452722468016115544211262068281082491409375}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{26}+\frac{119195852961911610261236922206512921804877238225972308271295762575622301848499354087652228984375}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{24}-\frac{648705870199984056527684484837810503148136610357443937072556122139140385945947711597096852109375}{282733943235299689621827862838197660153989988160624453758322}\cdot t^{22}+\frac{5541682051001726042978710648722706228280734199605255402561774963005718083223226889670865477390625}{282733943235299689621827862838197660153989988160624453758322}\cdot t^{20}-\frac{73158146107495777283165409886560894765897068012710116076579816701768799620776246176513184819765625}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{18}+\frac{365824213267915985670125997764403343233518020381655162585091005731340775577037968031316943106015625}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{16}-\frac{337759620152323044340686035432792911562880570895605146716783696288875996344319601976384709566015625}{141366971617649844810913931419098830076994994080312226879161}\cdot t^{14}+\frac{890973494967435964903096033963096529063366890373146756398463553141083490164425143751264799935937500}{141366971617649844810913931419098830076994994080312226879161}\cdot t^{12}-\frac{6417382648111294718092783436413837505144315807783471194103484156121964730167335512325953303617484375}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{10}+\frac{7401941780673681563614877313638509127866991507254489097356668557302084069848092434054322529857109375}{565467886470599379243655725676395320307979976321248907516644}\cdot t^8-\frac{2491486312349906606203601953419755331068570423456215044507572632218895056199136103649176482531015625}{282733943235299689621827862838197660153989988160624453758322}\cdot t^6+\frac{847335992218394425614318893353462619561250434339540355625401298438747375623858005051074110010546875}{282733943235299689621827862838197660153989988160624453758322}\cdot t^4-\frac{225265444131559660069100055029893479128732840061620884403503547992388035225307910268641281422265625}{565467886470599379243655725676395320307979976321248907516644}\cdot t^2+\frac{5484937826469426761090580883942370416771820459429497666030730388927646928323064709801822892265625}{565467886470599379243655725676395320307979976321248907516644}$

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.