Rule: Q[1, 24, 26]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{25}-\frac{300}{49}\cdot t^{23}+\frac{37950}{2303}\cdot t^{21}-\frac{25300}{987}\cdot t^{19}+\frac{360525}{14147}\cdot t^{17}-\frac{9806280}{580027}\cdot t^{15}+\frac{8171900}{1077193}\cdot t^{13}-\frac{49031400}{21460999}\cdot t^{11}+\frac{67418175}{150226993}\cdot t^9-\frac{8171900}{150226993}\cdot t^7+\frac{2451570}{665290969}\cdot t^5-\frac{2228700}{19293438101}\cdot t^3+\frac{185725}{173640942909}\cdot t$
• $P_3$:
  $t^{51}-\frac{33099}{2597}\cdot t^{49}+\frac{555059112}{7261265}\cdot t^{47}-\frac{12169295504}{42429945}\cdot t^{45}+\frac{868512532877973138}{1150543188320075}\cdot t^{43}-\frac{8094970977445642242}{5464863698763425}\cdot t^{41}+\frac{140044046262070547061309232}{62283883966850627349125}\cdot t^{39}-\frac{2309280244977777433618755912}{854116758454504057563875}\cdot t^{37}+\frac{53585806447372097014324505114956059}{20481964906911736883099858730625}\cdot t^{35}-\frac{8597110189167077621863994148250499}{4176824030015256332374869716575}\cdot t^{33}+\frac{35138136046576921936724330913510756812492095344}{26522796976384682781745397664377752908690625}\cdot t^{31}-\frac{6106950307690027149027172299538941041730019359168}{8726933558789846899690954144694569660140753125}\cdot t^{29}+\frac{29538538036415950120768748482641435372111229709521615588}{97351587507311568676570310209314860482817147196140625}\cdot t^{27}-\frac{95183333041914839044923504240047458514016333864042876}{883347738039293466847838801762315974249154049203125}\cdot t^{25}+\frac{715253826309052244894865022649376456668400491758217088}{22931707279500058399369895293749722691508039117313125}\cdot t^{23}-\frac{32438863042818263141974962423799695790307798014986256}{4441318801167995500273220827643226924442268445645625}\cdot t^{21}+\frac{5831788944653886377012518095650948059967946259492689}{4260040482752975275772273038759829907118094223374375}\cdot t^{19}-\frac{1588501593766950853138330485732417864525586876961631}{7847442994544954455369976650347055092059647253584375}\cdot t^{17}+\frac{7816489084936243971114676821082910286393412418804872}{337440048765433041580908995964923368958564831904128125}\cdot t^{15}-\frac{71921346217773558370454431784057678791812322628663856}{35971109198395162232524898969860831130983011080980058125}\cdot t^{13}+\frac{347872832952964829506146780127254618788243717347014}{2767008399876550940963453766912371625460231621613850625}\cdot t^{11}-\frac{1684878886459168216293826525883526306936771747610126}{307137932386297154446943368127273250426085709999137419375}\cdot t^9+\frac{7199613989887729957954222242516917317615984724592}{46536050361560174916203540625344431882740259090778396875}\cdot t^7-\frac{2028293685339227218822227941494362192655836981624}{804408870535540166408661202238096608258795907140598003125}\cdot t^5+\frac{801596505597473951227847421374548721016397963}{41217644605953297782923135982447925381855658051832294375}\cdot t^3-\frac{175351815396389822156450403278309407220007693}{3908992295197030322169656328713777572025175786591338404375}\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.