Rule: Q[1, 2, 40]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{43}-\frac{2807153741979615133}{258514102252430055}\cdot t^{41}+\frac{229747488198109461902}{4187928456489366891}\cdot t^{39}-\frac{993669601400192092558}{5804321895836140077}\cdot t^{37}+\frac{7863293549110856669501}{21282513618065846949}\cdot t^{35}-\frac{186787319153460529602553}{319237704270987704235}\cdot t^{33}+\frac{2485710024507768939613096}{3530962486633651880175}\cdot t^{31}-\frac{32960826972593423722981448}{50139667310197856698485}\cdot t^{29}+\frac{1669533953693869300348486994}{3459637044403652112195465}\cdot t^{27}-\frac{2406886355652454500869294614}{8585025258334988574707265}\cdot t^{25}+\frac{28923094319363050315875548}{223957180652217093253233}\cdot t^{23}-\frac{474242830913750982734292148}{10078073129349769196395485}\cdot t^{21}+\frac{552207297677627161992400342}{40984164059355728065341639}\cdot t^{19}-\frac{2416498744575773547331016242}{806021893167329318618385567}\cdot t^{17}+\frac{1233090974327058850085999416}{2418065679501987955855156701}\cdot t^{15}-\frac{574316787859105448787251720}{8866240824840622504802241237}\cdot t^{13}+\frac{13971533575161096208650277993}{2349553818582764963772593927805}\cdot t^{11}-\frac{48249465211960197588620399}{128157481013605361660323305153}\cdot t^9+\frac{1528715034585807436433494}{99678040788359725735807015119}\cdot t^7-\frac{15376605972467019966946}{42719160337868453886774435051}\cdot t^5+\frac{1370418295555383073306411}{343333891635448763888006134504887}\cdot t^3-\frac{53011847975560514091649}{4005562069080235578693404902557015}\cdot t$

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.