Rule: Q[4, 46]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{50}-\frac{1121980732008792033190312096305}{20503808819526530800649983688}\cdot t^{48}+\frac{480281995426159850406428225604668}{1492866132932237607702587957073}\cdot t^{46}-\frac{1016799353872841196886563563040166665}{860388514613279607905924859259739}\cdot t^{44}+\frac{21661819893706041696400992776037345285}{7123216539589012567779284881313188}\cdot t^{42}-\frac{171903634334298102850559661372674899145}{29510468521154480637942751651154636}\cdot t^{40}+\frac{83130368528193117369275314299976034895}{9647653170377426362404361116723631}\cdot t^{38}-\frac{424702468421585406446789897891249750076}{42145011217964546741029577509897967}\cdot t^{36}+\frac{4102140236297674871611973862590557874905}{433491543956206766479161368673236232}\cdot t^{34}-\frac{101624097480215531381077275776844802816715}{14101224929869549521351543345664684488}\cdot t^{32}+\frac{594027037215752828386581295170599320820}{132672815200385546571855918574802139}\cdot t^{30}-\frac{93678701202768308376363546696267676838}{41174321958740342039541491971490319}\cdot t^{28}+\frac{11565007653756136575743072272550268461}{12233315030476373499741672421321910}\cdot t^{26}-\frac{55634294718754689351521916858081849865}{173713073432764503696331748382771122}\cdot t^{24}+\frac{297950076388023780961065094337194472210}{3387404931938907822078469093464036879}\cdot t^{22}-\frac{209829254856220201538725903049151506220}{10807434782852705908536068060099546233}\cdot t^{20}+\frac{26773356086667400298360998334230025629775}{7867812521916769901414257547752469657624}\cdot t^{18}-\frac{4527928180485104691329513274194057664193}{9719062527073656937041141676635403694712}\cdot t^{16}+\frac{3612059074135568479730775847668537313120}{74107851768936634144938705284344953172179}\cdot t^{14}-\frac{1030025532052027084748557016024965198515}{272271704484408219953749162638087868247969}\cdot t^{12}+\frac{38950422736341337495700188326072679478935}{186233845867335222448364427244452101881610796}\cdot t^{10}-\frac{8463101788677942085021812164758919515}{1089086817937632879814996650552351472991876}\cdot t^8+\frac{6960134614671138036683292725256056017}{39168229487971296784775058110936354760814969}\cdot t^6-\frac{30211079608421707302813033095531635160}{13983057927205752952164695745604278649610943933}\cdot t^4+\frac{285343520231366085601114603301409915}{27270441330669926155465476279984463834067114536}\cdot t^2-\frac{16245460387990534478471765086415}{1925310399530964228046561549798692388706529688}$

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.