Rule: Q[1, 2, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^9-\frac{117}{4}\cdot t^7+\frac{945}{8}\cdot t^5-\frac{2205}{16}\cdot t^3+\frac{945}{32}\cdot t$
• $P_4$:
  $2\cdot t^{19}-\frac{23713751}{205892}\cdot t^{17}+\frac{2134183615}{823568}\cdot t^{15}-\frac{48885080515}{1647136}\cdot t^{13}+\frac{623352876985}{3294272}\cdot t^{11}-\frac{4536269518165}{6588544}\cdot t^9+\frac{18427952550645}{13177088}\cdot t^7-\frac{38805894891225}{26354176}\cdot t^5+\frac{36681698574675}{52708352}\cdot t^3-\frac{11110847880825}{105416704}\cdot t$
• $P_5$:
  $2\cdot t^{35}-\frac{148158172019154347566494279532305444494687200256542484844439972024607051000023761563231}{385760606209899831860610471660979420398054611050129842754406267835781132157028090276}\cdot t^{33}+\frac{2249942320220592204173182865179529289145984970438942004160704874997340053778177337020913259}{69436909117781969734909884898976295671649829989023371695793128210440603788265056249680}\cdot t^{31}-\frac{220849158772970079249588044514404572697676391214019057797593782286207915104784526104267559039}{138873818235563939469819769797952591343299659978046743391586256420881207576530112499360}\cdot t^{29}+\frac{14076452535407047075509904706929932084194209883569653124917820365324652269134990345424626592113}{277747636471127878939639539595905182686599319956093486783172512841762415153060224998720}\cdot t^{27}-\frac{3079461704370215575368823985946098203044130613330964437033194113796741253296061531689893628203229}{2777476364711278789396395395959051826865993199560934867831725128417624151530602249987200}\cdot t^{25}+\frac{13621590005974628394299390435466707875960413189403142442133883552507558252569258603353414031836829}{793564675631793939827541541702586236247426628445981390809064322405035471865886357139200}\cdot t^{23}-\frac{7555344735732247770778736796311822778855080357658901316591419468071013675725945354433109059803407}{39537030102651655365073244070591485079942963694817578189775446667866535964848430604800}\cdot t^{21}+\frac{3219710580700670279502708780755276042659877667713327453155485017016560499238619994520958078064961}{2091906354637653723019748363523358998938781147873945935966954850151668569568700032000}\cdot t^{19}-\frac{94703184350745630527408004926675491861812450062856179314573920985767025554447829325616105822169860877}{10580862341757252531033887222701149816632355045946418544120857632067139624878484761856000}\cdot t^{17}+\frac{157484513545995039812258087014296855688128394169414274752888698243122811598842273074780125572399172993}{4232344936702901012413554889080459926652942018378567417648343052826855849951393904742400}\cdot t^{15}-\frac{23549631437656828001609343706484598645025341463453683544660303514393391646415889277922730696464830187}{217043330087328257046848968670792816751432924019413713725556053991120812818020200243200}\cdot t^{13}+\frac{93354849639900358921608632783963512574570620469839157037326776142611274152386412728501470282091552853}{434086660174656514093697937341585633502865848038827427451112107982241625636040400486400}\cdot t^{11}-\frac{4883263925242950190669085624551426689401578018559150322810148516683487563072259572222768280960294573}{17717822864271694452803997442513699326647585634237854181678045223764964311675118387200}\cdot t^9+\frac{13537565622105100537332391567346142747089590000147244485599043633820513434062805161738407228679234793}{64309134840689853939807101828383056815239384894641100363127719701072833427561540812800}\cdot t^7-\frac{916695994687218333091656821821092731491782773637716223198067748233865557741850872806864840043001917}{11024423115546832103966931742008524025469608839081331490821894805898200016153406996480}\cdot t^5+\frac{281593491909388686402915463907712078147402844378914597860805998856747021879331968381790179022242211}{22048846231093664207933863484017048050939217678162662981643789611796400032306813992960}\cdot t^3-\frac{4733364936815051007936085288803863817032716310637460684423752827270817573558587806396618867308523}{14699230820729109471955908989344698700626145118775108654429193074530933354871209328640}\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.