Rule: Q[6, 51]

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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{57}-\frac{203586876292535540654266768920639615848732915705165690965}{141049776424247813923944329821556430467928027552521411}\cdot t^{55}+\frac{3134687978340154952173007396499728343632914762768811785987685}{3244144857757699720250719585895797900762344633707992453}\cdot t^{53}-\frac{1294045910180305324524661489377233599829465986825938290088028495}{3244144857757699720250719585895797900762344633707992453}\cdot t^{51}+\frac{369455479212914295570555882674778122707047991204971215436788241750}{3244144857757699720250719585895797900762344633707992453}\cdot t^{49}-\frac{77556907010291924541881052888170174811126869930513608322640449617050}{3244144857757699720250719585895797900762344633707992453}\cdot t^{47}+\frac{11493956411216032368282012764831124869267160441834469449483229806750}{3001059072856336466466900634501200648253787820266413}\cdot t^{45}-\frac{1439804255168529847472395730306155781681763165549988649988520053230250}{3001059072856336466466900634501200648253787820266413}\cdot t^{43}+\frac{143353643781945117787937000243803224216658202573045199773572420983807375}{3001059072856336466466900634501200648253787820266413}\cdot t^{41}-\frac{11471242786205005579627598437124392525793802518321441780352279351646025625}{3001059072856336466466900634501200648253787820266413}\cdot t^{39}+\frac{743177651017558247715804334446564957498101614528989868374099845031600582375}{3001059072856336466466900634501200648253787820266413}\cdot t^{37}-\frac{39154530207761771578621716735483812974780216441291272301623922394790058393125}{3001059072856336466466900634501200648253787820266413}\cdot t^{35}+\frac{1681049393587204823783903929440793733476414226145018139593688202606463966232500}{3001059072856336466466900634501200648253787820266413}\cdot t^{33}-\frac{58816813739828245871323564961635712721806750378175833498913682602937886959777500}{3001059072856336466466900634501200648253787820266413}\cdot t^{31}+\frac{1673939212411802247984463180268382939463639071772766717126763745860309062779912500}{3001059072856336466466900634501200648253787820266413}\cdot t^{29}-\frac{38608874329883649283023423027179569040307526873350603678567549964848199165776157500}{3001059072856336466466900634501200648253787820266413}\cdot t^{27}+\frac{717630183337755386221706418854208834761992229985824814232015464663210122223781546875}{3001059072856336466466900634501200648253787820266413}\cdot t^{25}-\frac{10666350011559551998563946657320205835898396395529465834486883506050530110732048328125}{3001059072856336466466900634501200648253787820266413}\cdot t^{23}+\frac{125485611181715296298573002452157708819520445830743644735223860216845644148424615796875}{3001059072856336466466900634501200648253787820266413}\cdot t^{21}-\frac{1153126681564151131472715832986689437943163563286093954334336732337994583566983165390625}{3001059072856336466466900634501200648253787820266413}\cdot t^{19}+\frac{8135868151141290903170092673235325281246583842883080837220472377614833153969830932093750}{3001059072856336466466900634501200648253787820266413}\cdot t^{17}-\frac{43092930625027237964673288030827093082944143799029104577292621665446173297562564455156250}{3001059072856336466466900634501200648253787820266413}\cdot t^{15}+\frac{166277160807902128800544597295911233973377558878503113541691981297126111783425525065468750}{3001059072856336466466900634501200648253787820266413}\cdot t^{13}-\frac{448442456011557295663309792539719764772613508541684354363088373906699283981204323392656250}{3001059072856336466466900634501200648253787820266413}\cdot t^{11}+\frac{796448568064265826588256552731814562453830339243550428222656975558309740024448022578515625}{3001059072856336466466900634501200648253787820266413}\cdot t^9-\frac{850091796715687575425240504927023261001213283360958977535183864016280053459031970975359375}{3001059072856336466466900634501200648253787820266413}\cdot t^7+\frac{466550268245167084752698356648390805270226131180317092495794897012752493826861516680390625}{3001059072856336466466900634501200648253787820266413}\cdot t^5-\frac{95028747902755215175904123448225393698345379376542457130770169160596273441813997034921875}{3001059072856336466466900634501200648253787820266413}\cdot t^3+\frac{1870172146981008760171334686160876806834847998167345385345783276541945204045102448750000}{3001059072856336466466900634501200648253787820266413}\cdot t$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.