Rule: Q[11, 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.

• $P_1$:
  $\frac{88179}{256}\cdot t^{11}-\frac{230945}{256}\cdot t^9+\frac{109395}{128}\cdot t^7-\frac{45045}{128}\cdot t^5+\frac{15015}{256}\cdot t^3-\frac{693}{256}\cdot t$
• $P_2$:
  $\frac{88179}{256}\cdot t^{35}-\frac{995857016250626234356218371658836515}{326328765124867415775814435903232}\cdot t^{33}+\frac{504392249728239404926268657194618635}{40791095640608426971976804487904}\cdot t^{31}-\frac{1238017849793681678478079965206392685}{40791095640608426971976804487904}\cdot t^{29}+\frac{12416741880991321227985384111210460245495}{246459799860556115764683852715915968}\cdot t^{27}-\frac{1272422947490770525157203912083006539525457}{21277696054628011327684372617807411904}\cdot t^{25}+\frac{463765281153452114114004336626586357699873225}{8862160406752566717980541195316787058016}\cdot t^{23}-\frac{304026128970431073603511393890920798099944575}{8862160406752566717980541195316787058016}\cdot t^{21}+\frac{4517746162276697384288755115024770331121975}{266531140052708773473098983317798107008}\cdot t^{19}-\frac{98764675298687759334604928248086981576225}{15678302356041692557241116665752829824}\cdot t^{17}+\frac{12052530149347835649291043159736874129187695}{6910211763425375994604022170430559744928}\cdot t^{15}-\frac{4534817373947274601773787064436555527681475}{12833250417789983989978898316513896669152}\cdot t^{13}+\frac{1223709802603946600356079686953417828951709275}{24033716513193457709232789108757486792859584}\cdot t^{11}-\frac{840730653029414841126019646232946860781379675}{168236015592354203964629523761302407550017088}\cdot t^9+\frac{26299229386669536932956535738261598019642725}{84118007796177101982314761880651203775008544}\cdot t^7-\frac{134533381114131023831821711525665243243045}{12016858256596728854616394554378743396429792}\cdot t^5+\frac{18134952256160634747841724214129589056525}{96134866052773830836931156435029947171438336}\cdot t^3-\frac{91208639313077909261725487515091157675}{96134866052773830836931156435029947171438336}\cdot t$

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.