Rule: Q[2, 6, 33]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{41}-\frac{288186070490653111244297565045552446671359502050992690057}{18603692508983255765793489431098235947874776060032661972}\cdot t^{39}+\frac{29459632650961661304738599608623426942015174882264560912604907}{397579512609481158970772662632000400442031839178958019003612}\cdot t^{37}-\frac{2857738734687905542007287827630021427327249962577798159791864005}{13120123916112878246035497866856013214587050692905614627119196}\cdot t^{35}+\frac{3814457136863553361730413873137776683229937295598172011134524019235}{8664904694884262304488872376925049870147990764757522345881720444}\cdot t^{33}-\frac{553348309869726862646577557049124040042547383384554712708145078703}{853361826011328863320873794697164002363059696529149928003502771}\cdot t^{31}+\frac{49432340519941600369028515823804082200756902999720051082325645807}{68661296345739103945357661642300551914269170985104017195684131}\cdot t^{29}-\frac{9929822360863409323577580639718931026012096402829894702327998219397}{16155022154490329171143438389267001286114474944638045188755966251}\cdot t^{27}+\frac{1107972839721182036033279732545697877748344341152379722030638727850}{2715516544486978407685079387369666882851151059070212724035903159}\cdot t^{25}-\frac{8042233808326839771592236180407586538548390512864686620199172728075}{38017231622817697707591111423175336359916114826982978136502644226}\cdot t^{23}+\frac{6334241034304734941211667238400377386069280784175209181954251845}{74011482718009794369093662731684626268493409786469133296241358}\cdot t^{21}-\frac{336107858679530678303704949841602165010452066280339741529578744905}{12514989291983465704983409350486290851400957054845328206426336298}\cdot t^{19}+\frac{80872217213767415417356403713858652769251224687072295433869597755}{12514989291983465704983409350486290851400957054845328206426336298}\cdot t^{17}-\frac{18258512281241281405036206088757940129558404019264936835416290525}{15590706999335334395191196394249870806406277009002230901226029117}\cdot t^{15}+\frac{10720141869482012611835006865584898342244567032485664131493076775}{68832441105909061377408751427674599682705263801649305135344849639}\cdot t^{13}-\frac{7052283425141978515149482391696111274183973319992052317535110155}{481827087741363429641861259993722197778936846611545135947413947473}\cdot t^{11}+\frac{10258500280796162962202026680002179164878188393032882881194130599445}{11154121871362475627689218401123762070510468385658502062587742915291778}\cdot t^9-\frac{87937840322518114473757098112063257926555423075959876498341792485}{2478693749191661250597604089138613793446770752368556013908387314509284}\cdot t^7+\frac{3349300606451558359285521304346691595958225565221948025436676975}{4603288391355942322538407594114568473544002825827318311544147869802956}\cdot t^5-\frac{82279582293286562482463236246363915434292583099780531701272275}{13809865174067826967615222782343705420632008477481954934632443609408868}\cdot t^3+\frac{263314437147095479538277960938569783289620964629807716264625}{32223018739491596257768853158801979314808019780791228180809035088620692}\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.