Rule: Q[2, 5, 44]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^7-\frac{53}{3}\cdot t^5+\frac{215}{3}\cdot t^3-55\cdot t$
• $P_3$:
  $t^{51}-\frac{502801104113177632431699760962800039726305523197440897060431638973}{441205073237585111427986598071543479440417793326604661306488215}\cdot t^{49}+\frac{1578648344836693772765510286824389712465748760765073651756033524771339}{2647230439425510668567919588429260876642506759959627967838929290}\cdot t^{47}-\frac{503867042966654807842557410376747824396673842085911962738813493936065801}{2647230439425510668567919588429260876642506759959627967838929290}\cdot t^{45}+\frac{2442320492300985512437979835094949247982001421045204714070626175476797009}{58827343098344681523731546409539130592055705776880621507531762}\cdot t^{43}-\frac{9429091354233355031527991495031583927646842827348282245342427198885465751}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^{41}+\frac{1122695456505320414296696019614199303262168053123764658509494574071168080233}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^{39}-\frac{102864654767907028028524881724921997713096609682385776580269122840769024019099}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^{37}+\frac{7358912885180672359380219917173250546849355472340251618576003897967460566361081}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^{35}-\frac{414777971664272962311676291438951672762847650279877540245713829824128710409224215}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^{33}+\frac{9254435879929143477638519776476018511091857215662559690204510782845868693610380955}{717406623150544896630872517189501592586045192400983189116241}\cdot t^{31}-\frac{327436308925677321056070661482031501009178932193023187407841986871272754205504433065}{717406623150544896630872517189501592586045192400983189116241}\cdot t^{29}+\frac{9172624170635292761088268343119128239022270991648846358983400634191291698626662741445}{717406623150544896630872517189501592586045192400983189116241}\cdot t^{27}-\frac{202595193177776064810482061291945960611090434717381661527632653783114151947108185282155}{717406623150544896630872517189501592586045192400983189116241}\cdot t^{25}+\frac{3503515113744404513682514953241690798866056186857441444231891709555390205693523507133625}{717406623150544896630872517189501592586045192400983189116241}\cdot t^{23}-\frac{46967162539282914228537165325081273169099960985083571215453007008186421343621787408278875}{717406623150544896630872517189501592586045192400983189116241}\cdot t^{21}+\frac{481634704474466940522161036216038796615078573836684115280559627769417733149372809060592250}{717406623150544896630872517189501592586045192400983189116241}\cdot t^{19}-\frac{3713480797100681575184408829932408495297879590227556073709524867083501707511478311778039250}{717406623150544896630872517189501592586045192400983189116241}\cdot t^{17}+\frac{42116610256241757962203702323850437178982826588543882906261416564058781201408511564071870875}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^{15}-\frac{170829067366143724909574776874798516776125015505559465161527695580501543283320396940118105625}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^{13}+\frac{478443700645597413324555951381348023304569186064074054638290237438917310499473830846786488125}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^{11}-\frac{884839217779094461151583205591670638725305015574576249854656083853450494439105826414928451875}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^9+\frac{1019735435000173567567120060098283728257090768966904321912110976940879198724858053717858543125}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^7-\frac{673858582897466298140717704369352787723460028257109961088543289073291498794044050963328269375}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^5+\frac{218723989830113167227044348670347886187337668236811373747945748063243474216680227475279090625}{1434813246301089793261745034379003185172090384801966378232482}\cdot t^3-\frac{22941860727408634407145518307317406655924897303854607634057799027572598365988321418988909375}{1434813246301089793261745034379003185172090384801966378232482}\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.