Rule: Q[4, 10, 15]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{14}-\frac{436215}{27784}\cdot t^{12}+\frac{12954799}{583464}\cdot t^{10}-\frac{3039465}{194488}\cdot t^8+\frac{2679105}{472328}\cdot t^6-\frac{8846695}{8974232}\cdot t^4+\frac{1485}{22952}\cdot t^2-\frac{273}{390184}$
• $P_3$:
  $\frac{35}{8}\cdot t^{29}-\frac{2402089014683800665037312007125125356817428388067478185}{71529207311958149593216150491297897582025343749358616}\cdot t^{27}+\frac{3270458960381271002652239024540054871822069537124442771674}{28227213435481484783222923387628432833306751277090643839}\cdot t^{25}-\frac{26784017695434811917989523247349936218418708957615366101825}{112908853741925939132891693550513731333227005108362575356}\cdot t^{23}+\frac{64608188725953743826299168956446993630331783961430990684425}{201591075963845183251385395260713957354976730746833689032}\cdot t^{21}-\frac{383704505548967349960794957906748309191944986918091711949125}{1276743481104352827258774169984521729914852628063280030536}\cdot t^{19}+\frac{24651159985763058005357894745578873859819238580385891724253125}{123071351875927484374970783806665870965213294120941967154036}\cdot t^{17}-\frac{3573376971053009630379729249569204285311019479388139328534825}{37404038315232862898275434294182764705113844291658833154658}\cdot t^{15}+\frac{4846821111105343170385721296334035111699016383715071764587125}{149616153260931451593101737176731058820455377166635332618632}\cdot t^{13}-\frac{216455952888509389821121221505963901273437032139524438819915625}{28277452966316044351096228326402170117066066284494077864921448}\cdot t^{11}+\frac{86766601393692989421684667518388113838281016329151573331845}{71407709510899101896707647288894368982490066374985045113438}\cdot t^9-\frac{57207597926925365588730160958906849319955607658461119459105}{469250662500194098178364539327020139027791864749901725031164}\cdot t^7+\frac{19637345589677880919542243058972336166541092217553875555659}{2815503975001164589070187235962120834166751188499410350186984}\cdot t^5-\frac{178019469735941922405743817047814577491418995739285248115}{947568970652565860089644335452630039196217388722023773251336}\cdot t^3+\frac{110011819037816453266295156219249909383108528007983596145}{72489026254921288296857791662126197998510630237234818653727204}\cdot t$

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.