Rule: Q[48]

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.

• $P_1$:
  $\frac{1608766753466574727105400775}{70368744177664}\cdot t^{48}-\frac{2387748549881968805493279045}{8796093022208}\cdot t^{46}+\frac{26573330635783201222425202275}{17592186044416}\cdot t^{44}-\frac{46040972127199465854238537275}{8796093022208}\cdot t^{42}+\frac{445407606758637529219094163975}{35184372088832}\cdot t^{40}-\frac{199665478891803030339593935575}{8796093022208}\cdot t^{38}+\frac{550450320238970707171507987095}{17592186044416}\cdot t^{36}-\frac{298436920611490142442383848425}{8796093022208}\cdot t^{34}+\frac{2066952005716616912471325172425}{70368744177664}\cdot t^{32}-\frac{90120270291441806310282813425}{4398046511104}\cdot t^{30}+\frac{101824201498122560376553308675}{8796093022208}\cdot t^{28}-\frac{23326998888660804740810394351}{4398046511104}\cdot t^{26}+\frac{34617692414679276441841909425}{17592186044416}\cdot t^{24}-\frac{2587888165344387946356545775}{4398046511104}\cdot t^{22}+\frac{1237685644295142061300956675}{8796093022208}\cdot t^{20}-\frac{116995160406008453555811825}{4398046511104}\cdot t^{18}+\frac{275388608340296821446757065}{70368744177664}\cdot t^{16}-\frac{3856983310088190776565225}{8796093022208}\cdot t^{14}+\frac{639317816426275702490775}{17592186044416}\cdot t^{12}-\frac{18820239020577250831575}{8796093022208}\cdot t^{10}+\frac{2971616687459565920775}{35184372088832}\cdot t^8-\frac{18009798105815551035}{8796093022208}\cdot t^6+\frac{463373879223384675}{17592186044416}\cdot t^4-\frac{1185099435353925}{8796093022208}\cdot t^2+\frac{8061900920775}{70368744177664}$

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.