Rule: Q[3, 6, 10, 16]

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.

• $P_1$:
  $t^3-3\cdot t$
• $P_2$:
  $t^9-\frac{117}{4}\cdot t^7+\frac{945}{4}\cdot t^5-\frac{2205}{4}\cdot t^3+\frac{945}{4}\cdot t$
• $P_3$:
  $t^{19}-\frac{23713751}{205892}\cdot t^{17}+\frac{2134183615}{411784}\cdot t^{15}-\frac{48885080515}{411784}\cdot t^{13}+\frac{623352876985}{411784}\cdot t^{11}-\frac{4536269518165}{411784}\cdot t^9+\frac{18427952550645}{411784}\cdot t^7-\frac{38805894891225}{411784}\cdot t^5+\frac{36681698574675}{411784}\cdot t^3-\frac{11110847880825}{411784}\cdot t$
• $P_4$:
  $t^{35}-\frac{148158172019154347566494279532305444494687200256542484844439972024607051000023761563231}{385760606209899831860610471660979420398054611050129842754406267835781132157028090276}\cdot t^{33}+\frac{2249942320220592204173182865179529289145984970438942004160704874997340053778177337020913259}{34718454558890984867454942449488147835824914994511685847896564105220301894132528124840}\cdot t^{31}-\frac{220849158772970079249588044514404572697676391214019057797593782286207915104784526104267559039}{34718454558890984867454942449488147835824914994511685847896564105220301894132528124840}\cdot t^{29}+\frac{14076452535407047075509904706929932084194209883569653124917820365324652269134990345424626592113}{34718454558890984867454942449488147835824914994511685847896564105220301894132528124840}\cdot t^{27}-\frac{3079461704370215575368823985946098203044130613330964437033194113796741253296061531689893628203229}{173592272794454924337274712247440739179124574972558429239482820526101509470662640624200}\cdot t^{25}+\frac{13621590005974628394299390435466707875960413189403142442133883552507558252569258603353414031836829}{24798896113493560619610673178205819882732082138936918462783260075157358495808948660600}\cdot t^{23}-\frac{7555344735732247770778736796311822778855080357658901316591419468071013675725945354433109059803407}{617766095353932115079269438602991954374108807731524659215241354185414624450756728200}\cdot t^{21}+\frac{3219710580700670279502708780755276042659877667713327453155485017016560499238619994520958078064961}{16343018395606669711091784090026242179209227717765202624741834766809910699755469000}\cdot t^{19}-\frac{94703184350745630527408004926675491861812450062856179314573920985767025554447829325616105822169860877}{41331493522489267699351121963676366471220136898228197437972100125262264159681581101000}\cdot t^{17}+\frac{157484513545995039812258087014296855688128394169414274752888698243122811598842273074780125572399172993}{8266298704497853539870224392735273294244027379645639487594420025052452831936316220200}\cdot t^{15}-\frac{23549631437656828001609343706484598645025341463453683544660303514393391646415889277922730696464830187}{211956377038406501022313445967571110108821214862708704810113333975703918767597851800}\cdot t^{13}+\frac{93354849639900358921608632783963512574570620469839157037326776142611274152386412728501470282091552853}{211956377038406501022313445967571110108821214862708704810113333975703918767597851800}\cdot t^{11}-\frac{4883263925242950190669085624551426689401578018559150322810148516683487563072259572222768280960294573}{4325640347722581653516600938113696124669820711483851118573741509708243240155058200}\cdot t^9+\frac{13537565622105100537332391567346142747089590000147244485599043633820513434062805161738407228679234793}{7850236186607648186011609109910041115141526476396618696670864221322367361762883400}\cdot t^7-\frac{916695994687218333091656821821092731491782773637716223198067748233865557741850872806864840043001917}{672877387423512701658137923706574952726416555119710174000359790399060059579675720}\cdot t^5+\frac{281593491909388686402915463907712078147402844378914597860805998856747021879331968381790179022242211}{672877387423512701658137923706574952726416555119710174000359790399060059579675720}\cdot t^3-\frac{4733364936815051007936085288803863817032716310637460684423752827270817573558587806396618867308523}{224292462474504233886045974568858317575472185039903391333453263466353353193225240}\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.