Rule: Q[1, 22, 24]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{23}-\frac{253}{45}\cdot t^{21}+\frac{1771}{129}\cdot t^{19}-\frac{33649}{1763}\cdot t^{17}+\frac{1144066}{68757}\cdot t^{15}-\frac{8008462}{848003}\cdot t^{13}+\frac{1144066}{326155}\cdot t^{11}-\frac{163438}{195693}\cdot t^9+\frac{245157}{2022161}\cdot t^7-\frac{572033}{58642669}\cdot t^5+\frac{572033}{1583352063}\cdot t^3-\frac{52003}{13194600525}\cdot t$
• $P_3$:
  $t^{47}-\frac{25897}{2205}\cdot t^{45}+\frac{113322499}{1755131}\cdot t^{43}-\frac{959379479497}{4346071709}\cdot t^{41}+\frac{19923582404121839}{37880467017393}\cdot t^{39}-\frac{31033185176017359211}{33458165316618889}\cdot t^{37}+\frac{777904517091072281912203}{619854394688769790165}\cdot t^{35}-\frac{28150706113321735291045224199}{21121290557261955091956309}\cdot t^{33}+\frac{2254343469394610310816304817317918}{1999855315553976709911821813459}\cdot t^{31}-\frac{3721590299650922816647877113053146554}{4858551721945698321083517297968957}\cdot t^{29}+\frac{33032056757621914801996133789319125487814}{78635049897541736741644991718141899679}\cdot t^{27}-\frac{49022717484142680083627096294919403652468218}{263446577743971821431669992477928907272525}\cdot t^{25}+\frac{27057042540972043621445397559351478848361227613573366}{407314686923986223036903458868680994440991298987749}\cdot t^{23}-\frac{91781004283626160584652118645486237892409678943042}{4829818422023552051820989630853924835268671529499}\cdot t^{21}+\frac{992851621227349356143624415404199331632635551042}{229991353429692954848618553850186896917555787119}\cdot t^{19}-\frac{400062290917326771283044443198408620382546062522}{520506747235620897815294621871475608813415728743}\cdot t^{17}+\frac{1983282610175769645723375904186654306405009139173}{18830097032347461891553305438291617612955921951585}\cdot t^{15}-\frac{25265701508380706962385779678720386111479407061}{2331345346862066710382790197121819323508828432101}\cdot t^{13}+\frac{37591139563952063579362994250868032263076444191}{46447572679790405999164820081119323445291274147243}\cdot t^{11}-\frac{122363205053757656871393242166404091881776253573}{2926197078826795577947383665110517377053350271276309}\cdot t^9+\frac{452992846639051282382511073396876694163568951}{325133008758532841994153740567835264117038919030701}\cdot t^7-\frac{192809354013253845885728369634015099514719119}{7199373765367512929870547112573495134020147492822665}\cdot t^5+\frac{30485965668473755185300287560102098208736249}{125269103517394724979747519758778815331950566375114371}\cdot t^3-\frac{303650596860758747970802930234565611318661}{459320046230447324925740905782188989550485410042086027}\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.