Rule: Q[4, 10, 13]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{14}-\frac{436215}{27784}\cdot t^{12}+\frac{12954799}{583464}\cdot t^{10}-\frac{3039465}{194488}\cdot t^8+\frac{2679105}{472328}\cdot t^6-\frac{8846695}{8974232}\cdot t^4+\frac{1485}{22952}\cdot t^2-\frac{273}{390184}$
• $P_3$:
  $\frac{35}{8}\cdot t^{27}-\frac{25463155296244159533708703496435305}{872318580442745751302365540738472}\cdot t^{25}+\frac{11201316710374758769017160705602021655}{129405106337218090875893226562626404}\cdot t^{23}-\frac{78658080889032339275458468028893361995}{523246734320055758759046524796706764}\cdot t^{21}+\frac{79161987505360064407895215315193193591069}{466785920035805932599617980740071643656}\cdot t^{19}-\frac{547381838910741180015872698980194837866771}{4201073280322253393396561826660644792904}\cdot t^{17}+\frac{4523096579422299782897414858717676553151646683}{65075139949603509261432521685393321744631110}\cdot t^{15}-\frac{65384715421642538685684225887984216097858443371}{2537930458034536861195868345730339548040613290}\cdot t^{13}+\frac{1147980121492249039555797906777438712934753096021}{175702877863929475005867808550561968710503997000}\cdot t^{11}-\frac{689147244240902283696906725639079019565115219439}{628625851913169899465438159480899488053136522600}\cdot t^9+\frac{5152508219481989599736610491357899671558039557}{44901846565226421390388439962921392003795465900}\cdot t^7-\frac{753454964188307932206797368578493745604321901}{111278489313822000837049612082022580183319198100}\cdot t^5+\frac{26089294085476527357993851437189505475407901}{140128468024812889942951363362546952823438990200}\cdot t^3-\frac{9570174998262527888503613913866400471925279}{6305781061116580047432811351314612877054754559000}\cdot t$

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.