Rule: Q[2, 4, 9, 16]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{15}-\frac{1280116003}{245021714}\cdot t^{13}+\frac{12427268373}{1715151998}\cdot t^{11}-\frac{61055366515}{12006063986}\cdot t^9+\frac{7331508745275}{3877958667478}\cdot t^7-\frac{195050681397}{553994095354}\cdot t^5+\frac{14996878941}{553994095354}\cdot t^3-\frac{264841293}{553994095354}\cdot t$
• $P_4$:
  $\frac{3}{2}\cdot t^{31}-\frac{198556732460582445302583528862752050934490689230299849426467064858703643339566259048500026206843940705}{17633460881101039514801522539581403538049140703835809053748402283188814251926353815237053530336061654}\cdot t^{29}+\frac{4708672298870587892749129978650494189820373764364143600774987504713897227507228231106990721752855586315}{123434226167707276603610657777069824766343984926850663376238815982321699763484476706659374712352431578}\cdot t^{27}-\frac{2863614056595024002285732388609921129144095826230494718499673196737455453422201324283109822756709689042455}{37153702076479890257686807990898017254669539462982049676247883610678831628808827488704471788418081904978}\cdot t^{25}+\frac{1240775322271176769185363912049476763812520875368745686922544995425422874819087480831522874533269955189633325}{12000645770703004553232838981060059573258261246543202045428066406249262616105251278851544387659040455307894}\cdot t^{23}-\frac{50610880582602857695720824479078227379739883186148255721079598975754819178601284484492688683970617629680075}{521767207421869763184036477437393894489489619414921828062089843749967939830663099080501929898219150230778}\cdot t^{21}+\frac{180066246779700485118197662057335201501259402629068540783114390834479409442237393529830372265438376249573325}{2757912382087025891115621380740510585158730845478872519756760602678401967676362095139795915176301222648398}\cdot t^{19}-\frac{4619598422863414844876218596000832550000308749715693893916679049756701310589925515693381669623966287143575}{145153283267738204795559020038974241324143728709414343145092663298863261456650636586305048167173748560442}\cdot t^{17}+\frac{3919989280937024816702978983461354831359713003256975076309714134264387161400337793844652710011359235351725}{350075565528074493918701165976349640840581933946234592291105835014905512924863300002265116167889628881066}\cdot t^{15}-\frac{980407807381110054363573963831801348518989517349237486105184225829854357604631847562339322217106485370925}{350075565528074493918701165976349640840581933946234592291105835014905512924863300002265116167889628881066}\cdot t^{13}+\frac{32024942031448296878921246740835977834494707340230336344015527751953542235600107847436773522633024009315}{66230512397203282633267788157687769888758744260098436379398401219036178120920083784212319275006146004526}\cdot t^{11}-\frac{134575349903846226242673610705186485407946390865607549936990171818793312776916724963925205295279108388375}{2450528958696521457430908161834447485884073537623642146037740845104338590474043100015855813175227402167462}\cdot t^9+\frac{9302262057881978921554268606151588522262596572270048376083192219729411076226732879811111834654893919415}{2450528958696521457430908161834447485884073537623642146037740845104338590474043100015855813175227402167462}\cdot t^7-\frac{1130980947673984071733535156208929438050817453948043916242149164360036108175341852404468452814959815575}{8051738007145713360130126817456041739333384480763395622695434205342826797271855900052097671861461464264518}\cdot t^5+\frac{17912220081650637700416507830652645853455852016863916349356254979177659360992692204560346585198185435}{8051738007145713360130126817456041739333384480763395622695434205342826797271855900052097671861461464264518}\cdot t^3-\frac{1521122692125072142257479216231266998473718631523936047122127682279088104453100366097656698171133609}{152983022135768553842472409531664793047334305134504516831213249901513709148165262100989855765367767821025842}\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 Legendre type can be downloaded here packed into a single file.