Rule: Q[10, 23]

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.

• $P_1$:
  $\frac{46189}{256}\cdot t^{10}-\frac{109395}{256}\cdot t^8+\frac{45045}{128}\cdot t^6-\frac{15015}{128}\cdot t^4+\frac{3465}{256}\cdot t^2-\frac{63}{256}$
• $P_2$:
  $\frac{46189}{256}\cdot t^{33}-\frac{95932604690083189572522006261981}{65575168860537750200434973440}\cdot t^{31}+\frac{138309703238682566802478602944123493}{25718581227102905628610596583168}\cdot t^{29}-\frac{304870229001895088318553960465812661}{25718581227102905628610596583168}\cdot t^{27}+\frac{374095419465310546713621124536230569101}{21423578162176720388632626953778944}\cdot t^{25}-\frac{237379616120161881636675444902766421304775}{13089806257089976157454535068758934784}\cdot t^{23}+\frac{3646610171144993751853906677895844417235}{267138903205917880764378266709366016}\cdot t^{21}-\frac{14099153358598859087655436591614857693925}{1869972322441425165350647866965562112}\cdot t^{19}+\frac{5720545305554564483091671598401830913475}{1869972322441425165350647866965562112}\cdot t^{17}-\frac{1292389529323557154664314140279330254115}{1429978834808148655856377780620723968}\cdot t^{15}+\frac{413696407944972167120058732580173169301955}{2169277892403961510934125093201638259456}\cdot t^{13}-\frac{37774156986176925013672008734671364667639}{1357489907720566350917196783895411883776}\cdot t^{11}+\frac{133992941589976955027112176103055308483315}{50227126585660954983936281004130239699712}\cdot t^9-\frac{1110991666537330620246453441401546568165}{7175303797951564997705183000590034242816}\cdot t^7+\frac{4844175875970578970105702440479859775}{1025043399707366428243597571512862034688}\cdot t^5-\frac{409814670816282179450812046660449785}{7175303797951564997705183000590034242816}\cdot t^3+\frac{2060262339948963568747482107514543}{17938259494878912494262957501475085607040}\cdot t$

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.