Rule: Q[1, 26, 28]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{27}-\frac{351}{53}\cdot t^{25}+\frac{17550}{901}\cdot t^{23}-\frac{1480050}{44149}\cdot t^{21}+\frac{11100375}{296429}\cdot t^{19}-\frac{8436285}{296429}\cdot t^{17}+\frac{11248380}{749791}\cdot t^{15}-\frac{168725700}{30741431}\cdot t^{13}+\frac{42181425}{30741431}\cdot t^{11}-\frac{257775375}{1137432947}\cdot t^9+\frac{185598270}{7962030629}\cdot t^7-\frac{1533870}{1137432947}\cdot t^5+\frac{1278225}{35260421357}\cdot t^3-\frac{294975}{1022552219353}\cdot t$
• $P_3$:
  $t^{55}-\frac{41525}{3021}\cdot t^{53}+\frac{291057745}{3258747}\cdot t^{51}-\frac{11916339513485}{32658970743}\cdot t^{49}+\frac{110757963998332970}{105349174992027}\cdot t^{47}-\frac{3774047112413002942}{1660930609980681}\cdot t^{45}+\frac{3754235236038789696314773070}{981638198083131772905423}\cdot t^{43}-\frac{484921069825271794949203004750}{94390044338401459616170647}\cdot t^{41}+\frac{40019176945287119888457437782524085}{7146129822891968593173533674383}\cdot t^{39}-\frac{336234049416972410716431975586979417419885}{67111999257721707330652281158325995391}\cdot t^{37}+\frac{10286469913896338359073480601968698941692838007}{2775471144437614494529933724287294506418095}\cdot t^{35}-\frac{10293692852443821345625603719464181711197844605}{4520053006655543605377320636696451053309469}\cdot t^{33}+\frac{177215686449236857041892148366113068871041452818064071252}{152147148717288841890511376063358516647216173792110561}\cdot t^{31}-\frac{309425953379633262744157299353972866912865919011089012844}{624067585185306341550906463108515205999623660740344311}\cdot t^{29}+\frac{314829558822811220056591948634941160155713979071727866416812748}{1796014239123159405842004416281517432403628168511678572012089}\cdot t^{27}-\frac{1311356395003162736854218258824955517257528213008575109437604}{25584248420557826294045646955577171401761085021533882792195}\cdot t^{25}+\frac{3340332995931200054995087473555473200236031329627593280222565}{271193033257912958716883857729118016858667501228259157597267}\cdot t^{23}-\frac{10149500086891938194370787442009252320042438395711165619769735}{4209387516220648967909892922143266609501925997325587794009753}\cdot t^{21}+\frac{76172276704357785644326113348915380710957857298992520131625}{200447024581935665138566329625869838547710761777408942571893}\cdot t^{19}-\frac{7848496509763958033318120695039575642197197915175394980375}{165280879918438180026537148989752323013024663219968777208403}\cdot t^{17}+\frac{403503639215875330444619693547511334667563320803563656346}{87501642309761389425813784759280641595130704057630529110331}\cdot t^{15}-\frac{228911163080355424600989033758247984596107104887821681870}{675333188083030210696665364424191618464983126188379211851529}\cdot t^{13}+\frac{19656218961274431250384093992390272843443707122716036845070}{1079857767744765306903967917714282397925508018775218359750594871}\cdot t^{11}-\frac{28633610536502160986135317323386243263008649742059116561970}{42114452942045846969254748790857013519094812732233516030273199969}\cdot t^9+\frac{19929203437017424820021017203779551504276998810941899659935}{1211960367998874929448553326314662944605061833072053405760084310219}\cdot t^7-\frac{12653356707447003997609017084837807832499674166224373}{54981643514897016261332546673078208256819027948648251406799633}\cdot t^5+\frac{60956414601791477856808387025401411407065251103083565}{39954737406556316355446812955428448723243796694683079310772010227}\cdot t^3-\frac{228771838098514615817226507879624246478211242796915}{75595113496911715921338336249003121293273474497452023296906667237}\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.