Rule: Q[5, 12, 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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{17}-\frac{15500107}{453038}\cdot t^{15}+\frac{14463685}{235828}\cdot t^{13}-\frac{754990808}{12911583}\cdot t^{11}+\frac{2466422101}{77469498}\cdot t^9-\frac{2971987447}{301270270}\cdot t^7+\frac{61205289431}{37615745140}\cdot t^5-\frac{683012759}{5642361771}\cdot t^3+\frac{39745277}{15046298056}\cdot t$
• $P_3$:
  $\frac{63}{8}\cdot t^{33}-\frac{357119827861575879523817160898812120678503011387011335775536542674041480747869}{5539987253303448857924276248914531888437454548043129635050252507812502710254}\cdot t^{31}+\frac{5806663358553543098087313190683548922907314323485160516944874459869664302158652277}{24209744296936071509129087207756504352471676374948476505169603459140636843809980}\cdot t^{29}-\frac{7057667150864891034870723711461362261619210793870404623941920825058165853728624253}{13148395609542866423061487018005687708669962169153051895049008775222932078965765}\cdot t^{27}+\frac{370123674342800831865923446704514326743730338046831491489469340725202907964269982299893}{459349580931703361805250202779569230908470920454758567731349002358814623967152394300}\cdot t^{25}-\frac{1414646881089669598912532727124993701830881032935101817800839378363151974779081906121383}{1651538416365216548521338036762851219435533140158108881212557874634691963401900223814}\cdot t^{23}+\frac{156178682824909779073995967355000926887862397386931714887249783641945186100878570735438453671323}{235341609396217446571422178120148090921799366211725265233727577252142099855828728884807294500}\cdot t^{21}-\frac{3189551999022054031404031309585233072372040682482941921030958898007464747486549607905581216192408}{8396652420957901040173241283643855101102770244482626427446208916960355634141889291282945971625}\cdot t^{19}+\frac{30017753406959790986058254797891750597716966852413557317121436560604569271140916669403802267717877671}{186312878639560078922454568040600677477574574072180551344581432489542964831467321384840904851441250}\cdot t^{17}-\frac{28126908534580575984734498528800115619852851870116870670248915322839685676838433811186615099686501327}{558938635918680236767363704121802032432723722216541654033744297468628894494401964154522714554323750}\cdot t^{15}+\frac{849278846299325589620309833994728948796785863856161219975145135983570290905793590096395849435780053}{74525151455824031568981827216240270991029829628872220537832572995817185932586928553936361940576500}\cdot t^{13}-\frac{75726086022747036374179786384564287656511331807392242783309815919440571481916905045956707626896641}{41562103696517248375009095947518612668074328062255661453791242632282661385481171693541432620706125}\cdot t^{11}+\frac{885456612782467723464568411525306232503471144229658067265523228738042810703927389455208803727789403}{4488707199223862824500982362332010168152027430723611437009454204286527429631966542902474723036261500}\cdot t^9-\frac{591450667592179640183727182774103932299825543297565234533899227318835156499951023180553698110404939}{43640208881343110793759550744894543301478044465368444526480804763896794454755230278218504251741431250}\cdot t^7+\frac{152457455792233320183316749454122370469689688653384167886474446531835634541472503406922820698302273}{286778515505969013787562762037878427409712863629564064031159574162750363559820084685435885082872262500}\cdot t^5-\frac{423165850918855996406547182609031086496725045812974801170232806538988776841319437676922072782342}{43016777325895352068134414305681764111456929544434609604673936124412554533973012702815382762430839375}\cdot t^3+\frac{68477498187654801489678671327112551668314595682597515383298554420922655179035898381972306633}{1236254519481205050927667039981778813564275532379289215335685061620478027824522202841357190374265000}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.