Rule: Q[2, 3, 34]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{39}-\frac{228761697464588906376122370873957}{16189849123139034364162472845472}\cdot t^{37}+\frac{211436862599813779228659835794152477}{3448437863228614319566606716085536}\cdot t^{35}-\frac{120091670840912356726543209812694095}{738950970691845925621415724875472}\cdot t^{33}+\frac{27915894059883076438416613405798975975}{94893620486344547615216802669425196}\cdot t^{31}-\frac{41319520074568678217966647989844017151}{107271049245432966869375516061089352}\cdot t^{29}+\frac{8370249481036642629772741043957157688073}{22205107193804624141960731824645495864}\cdot t^{27}-\frac{135521143880474532235519341131621881877}{482375904138918117044018746902911413}\cdot t^{25}+\frac{128315819226041805938317704649681054456675}{796884993637492729356718969883609654276}\cdot t^{23}-\frac{29590136946543733248991039147250066975375}{415766083636952728360027288634926776144}\cdot t^{21}+\frac{478801590964097837549756473052877842935}{19798384935092987064763204220710798864}\cdot t^{19}-\frac{3285572463984235364479301495234405269535}{524657200779964157216224911848836169896}\cdot t^{17}+\frac{957893821782295391782631745094684364405}{786985801169946235824337367773254254844}\cdot t^{15}-\frac{91059384190469003893332573651879566275}{524657200779964157216224911848836169896}\cdot t^{13}+\frac{3031845190204268938999362244958832096875}{172612219056608207724137995998267099895784}\cdot t^{11}-\frac{3268453465890139135368133307282550701005}{2718642450141579271655173436972706823358598}\cdot t^9+\frac{31282309233918088788583146395729311885}{604142766698128727034482985993934849635244}\cdot t^7-\frac{1522124737959478569222988279492478744215}{1217261368787201080870621147779779588465068768}\cdot t^5+\frac{11077752209152915567373756896161002975}{804630396316963426338207199379854304239621728}\cdot t^3-\frac{340610804504599380234456134011646125}{7912198897116807025659037460568567325022946992}\cdot t$

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.