Rule: Q[1, 4, 6, 22]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{10}{9}\cdot t^3+\frac{5}{21}\cdot t$
• $P_3$:
  $t^{11}-\frac{319}{117}\cdot t^9+\frac{15994}{5915}\cdot t^7-\frac{219098}{186745}\cdot t^5+\frac{23263}{112047}\cdot t^3-\frac{383}{37349}\cdot t$
• $P_4$:
  $t^{33}-\frac{2624182172905840234342452169007117406597471632012633961824101780693}{320964008380396297833034189556816696741341027588693344741661573125}\cdot t^{31}+\frac{20160004965559767902614016275124775410165605754945389304891457750971627}{663432605322279147620881669813940112164351904025829143581014471649375}\cdot t^{29}-\frac{1045894445447386975782404446087190001316131168871276242319633214683032815728}{15394953606503487620542559148032480302773785932919365276797440814623746875}\cdot t^{27}+\frac{31281734989750335137254084671877388665770139882418220444818595660533737754}{307021866796365849982330239419451174129391742251953153668325030491071875}\cdot t^{25}-\frac{20821159283308240295068905865644121648631241783221250269637714009847638997}{192400369859055932655593616702856069121085491811223976298817019107738375}\cdot t^{23}+\frac{13909779682952518623135204835753949028420275218524024715449049530898949299}{166044154809870188456197230853149758282580629919275486394869482243664625}\cdot t^{21}-\frac{1189108088430127628440627679704078413291421145664488594919487764277134794354}{24819647711818215312571576554668432916620028443647892942547395464898250375}\cdot t^{19}+\frac{2519421496155756156454915778993812159428812042075626492182781741386072829358}{124098238559091076562857882773342164583100142218239464712736977324491251875}\cdot t^{17}-\frac{1803300682177929279651385323719772144970949067512875276431527236805726427379}{284695959047326587408909260480020259925935620383019948458631889156185813125}\cdot t^{15}+\frac{335311542030313031636269645581770744267770286949040397029066462148169670527}{234083344105579638536214280839127769272435954537149735399319553306197224125}\cdot t^{13}-\frac{1518820913846981199370344158597368239640932624856445662081532031072869822996}{6644365690381452816912543817664472835502220555708327104796070397691290438625}\cdot t^{11}+\frac{491908956908616265515426116385441094343479725325620189925148084354303662378}{19933097071144358450737631452993418506506661667124981314388211193073871315875}\cdot t^9-\frac{130806188020909765211810108983888807000256221359454154803633839444692349877}{77517599721116949530646344539418849747525906483263816222620821306398388450625}\cdot t^7+\frac{5151658112273244621819634409619746030754980434347673083371931964765159}{78538601541151924549793662147334194273075893093479043791915725741031801875}\cdot t^5-\frac{7902885805108670682979730525669711453296196676429337118899911923806334}{6644365690381452816912543817664472835502220555708327104796070397691290438625}\cdot t^3+\frac{182827717558847373546972924241739764321803148462342086678132076619287}{28792251324986295539954356543212715620509622408069417454116305056662258567375}\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.