Rule: Q[20, 21]

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.

• $P_1$:
  $\frac{34461632205}{262144}\cdot t^{20}-\frac{83945001525}{131072}\cdot t^{18}+\frac{347123925225}{262144}\cdot t^{16}-\frac{49589132175}{32768}\cdot t^{14}+\frac{136745788725}{131072}\cdot t^{12}-\frac{29113619535}{65536}\cdot t^{10}+\frac{15058768725}{131072}\cdot t^8-\frac{557732175}{32768}\cdot t^6+\frac{334639305}{262144}\cdot t^4-\frac{4849845}{131072}\cdot t^2+\frac{46189}{262144}$
• $P_2$:
  $\frac{34461632205}{262144}\cdot t^{41}-\frac{15179907170505}{11272192}\cdot t^{39}+\frac{1549324011602367}{242352128}\cdot t^{37}-\frac{9140903435342360253}{489793650688}\cdot t^{35}+\frac{7896308459244085183667}{210611269795840}\cdot t^{33}-\frac{8460855361564525280207847}{153956838220759040}\cdot t^{31}+\frac{626731592174338689406893702177}{10306736757712601907200}\cdot t^{29}-\frac{68917880269506024435335452886519}{1329569041744925646028800}\cdot t^{27}+\frac{249389123506817786811639166016101503}{7241719380704028352036864000}\cdot t^{25}-\frac{9287258393976385286626256382576584631049}{518097226341460582001114175897600}\cdot t^{23}+\frac{44333764918741170512738555232648885774632460733}{6064399272695418063153066582080593920000}\cdot t^{21}-\frac{28266292786747463682403245967699053855386491}{12159196536732667795795622219710464000}\cdot t^{19}+\frac{34022591747514081329019258424378239480953}{59603904591826802920566775586816000}\cdot t^{17}-\frac{76225108295821168860264563632983810392221}{715246855101921635046801307041792000}\cdot t^{15}+\frac{110213867577390279683508524590346458277}{7450488073978350365070846948352000}\cdot t^{13}-\frac{16626174374040214341902162202041249649}{11246019734306943947276750110720000}\cdot t^{11}+\frac{1370844965287099409531210651905516619}{13495223681168332736732100132864000}\cdot t^9-\frac{7474732077970771145185413727060278471}{1668909328571150481775869716430848000}\cdot t^7+\frac{121798498072143375389920085866404611}{1072870282652882452570201960562688000}\cdot t^5-\frac{43681829000303649887373526634448413}{32186108479586473577106058816880640000}\cdot t^3+\frac{259857126789906079897953704351423}{53643514132644122628510098028134400000}\cdot t$

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.