Rule: Q[4, 38]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{42}-\frac{97243042869838832791731069}{2062620448608929012285768}\cdot t^{40}+\frac{81088366321701546613009626615}{343487328967014163652452732}\cdot t^{38}-\frac{206063406991591662229163852943}{282616156745011653638094020}\cdot t^{36}+\frac{1983710360454479681322639376323}{1275810079020338322137681576}\cdot t^{34}-\frac{85867582673563272944466312368529}{35361088981617184618393602184}\cdot t^{32}+\frac{63534916388094443146172176434519}{22100680613510740386496001365}\cdot t^{30}-\frac{17944325540801452623893765055689889}{6811429765084010187118067620693}\cdot t^{28}+\frac{3350402855594690405141416924761733719}{1770971738921842648650697581380180}\cdot t^{26}-\frac{204282525484520127008316676786221735}{190720033422352285239305893379404}\cdot t^{24}+\frac{11004712791161890582814347855389105}{22991940788070137153355058292774}\cdot t^{22}-\frac{32600719333053098402270811839424747}{193789215213734013149706919896238}\cdot t^{20}+\frac{196703176409922948995159095129274655}{4263362734702148289293552237717236}\cdot t^{18}-\frac{457076301879227625464656049063339859}{46896990081723631182229074614889596}\cdot t^{16}+\frac{12567768630299743021265620274089861845}{8078006541576895471138958102414732911}\cdot t^{14}-\frac{8730041489100158485523606004843675}{47798855275602931781887326049791319}\cdot t^{12}+\frac{335951080225325536998536035160687127}{22143906044042958214590710322703323784}\cdot t^{10}-\frac{18666605821358096562720155413835745}{22143906044042958214590710322703323784}\cdot t^8+\frac{45463252326974113036764400929471}{1581707574574497015327907880193094556}\cdot t^6-\frac{358007942028421941631239371569155}{687882622020961948805328241010052527348}\cdot t^4+\frac{408116908879792409490394786880265}{108685454279311987911241862079588299320984}\cdot t^2-\frac{82941385181609738083764709503}{18349492280922803153846028662787634950296}$

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.