Rule: Q[4, 42]

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^{46}-\frac{58150556269699455354703425525}{1192044575353714673205208984}\cdot t^{44}+\frac{270169689851449993205748104734557}{1064495805790867203172251622712}\cdot t^{42}-\frac{2493117999986844532286857514591103}{3046660409677309581492996023624}\cdot t^{40}+\frac{211613978989864646504531559591607045}{115538737074685663359695926126664}\cdot t^{38}-\frac{1451198726455484551776436228119880245}{480397906784219337127156745474024}\cdot t^{36}+\frac{5482218677898395559472679633660204075}{1441193720352658011381470236422072}\cdot t^{34}-\frac{528274698121729202464652823415314737}{141293501995358628566810807492360}\cdot t^{32}+\frac{14997285172133599566237258034698976951}{5157212822830589942688594473471140}\cdot t^{30}-\frac{40999399177907173916502434724507397781}{22727303405439634299158702541710748}\cdot t^{28}+\frac{2261436916251126872852981400625997385}{2525255933937737144350966949078972}\cdot t^{26}-\frac{60157459403362020298878030543278643975}{169192147573828388671514785588291124}\cdot t^{24}+\frac{19023098554081143237942552549596315257}{169192147573828388671514785588291124}\cdot t^{22}-\frac{4753165940958363792155576333812597989}{169192147573828388671514785588291124}\cdot t^{20}+\frac{735162045491439615611274600794849669265}{134169373026045912216511224971514861332}\cdot t^{18}-\frac{6490555033165591645570503352551516666055}{7915993008536708820774162273319376818588}\cdot t^{16}+\frac{1455096876333216826422155864299336379625}{15831986017073417641548324546638753637176}\cdot t^{14}-\frac{9092497912468918307388819044260472697}{1217845078236416741657563426664519510552}\cdot t^{12}+\frac{81220092104565445848182376747820284971}{193637367439590261923552584839658602177768}\cdot t^{10}-\frac{982033322986958773268249809076470845}{64545789146530087307850861613219534059256}\cdot t^8+\frac{282789520446973845347353227402255}{884188892418220374080148789222185398072}\cdot t^6-\frac{47102970247785497832996711050979925}{14624919776619003812246028808213220097814408}\cdot t^4+\frac{70116914736113801282319404187389997}{6859087375234312787943387511052000225874957352}\cdot t^2-\frac{10867813639967629873750291807569}{6859087375234312787943387511052000225874957352}$

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.