Rule: Q[2, 4, 6, 9]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{12}-\frac{1595}{364}\cdot t^{10}+\frac{318813}{66248}\cdot t^8-\frac{10310751}{4183088}\cdot t^6+\frac{2471775}{4183088}\cdot t^4-\frac{33827}{597584}\cdot t^2+\frac{31245}{29281616}$
• $P_4$:
  $\frac{3}{2}\cdot t^{21}-\frac{4993619531904582049233759017547}{653375242625340161842770385804}\cdot t^{19}+\frac{2330906295460902079025668691958876425}{139486467047113369791165678583752744}\cdot t^{17}-\frac{7285215703133166228647214786168265267}{355553739531857609271598788546820720}\cdot t^{15}+\frac{1043196650457059219808089275868495452399}{67524734476235929395094775642020495024}\cdot t^{13}-\frac{46301688044162483758054192468974371853}{6268874553496704320499514980028427920}\cdot t^{11}+\frac{799162700898803387210507561719688593}{359046797994873782675087428085894160}\cdot t^9-\frac{251078780988715835728911138059828663655}{618111030974775046001252177030802992912}\cdot t^7+\frac{18169329920409181893707707613750942261}{441507879267696461429465840736287852080}\cdot t^5-\frac{15607168952745261307116677412811118271}{8035443402672075598016278301400438907856}\cdot t^3+\frac{225983960123218315957162264090710645}{8035443402672075598016278301400438907856}\cdot t$

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.