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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^7-\frac{106}{3}\cdot t^5+\frac{215}{3}\cdot t^3-\frac{55}{2}\cdot t$
• $P_3$:
  $4\cdot t^{51}-\frac{1005602208226355264863399521925600079452611046394881794120863277946}{441205073237585111427986598071543479440417793326604661306488215}\cdot t^{49}+\frac{1578648344836693772765510286824389712465748760765073651756033524771339}{2647230439425510668567919588429260876642506759959627967838929290}\cdot t^{47}-\frac{503867042966654807842557410376747824396673842085911962738813493936065801}{5294460878851021337135839176858521753285013519919255935677858580}\cdot t^{45}+\frac{2442320492300985512437979835094949247982001421045204714070626175476797009}{235309372393378726094926185638156522368222823107522486030127048}\cdot t^{43}-\frac{9429091354233355031527991495031583927646842827348282245342427198885465751}{11478505970408718346093960275032025481376723078415731025859856}\cdot t^{41}+\frac{1122695456505320414296696019614199303262168053123764658509494574071168080233}{22957011940817436692187920550064050962753446156831462051719712}\cdot t^{39}-\frac{102864654767907028028524881724921997713096609682385776580269122840769024019099}{45914023881634873384375841100128101925506892313662924103439424}\cdot t^{37}+\frac{7358912885180672359380219917173250546849355472340251618576003897967460566361081}{91828047763269746768751682200256203851013784627325848206878848}\cdot t^{35}-\frac{414777971664272962311676291438951672762847650279877540245713829824128710409224215}{183656095526539493537503364400512407702027569254651696413757696}\cdot t^{33}+\frac{9254435879929143477638519776476018511091857215662559690204510782845868693610380955}{183656095526539493537503364400512407702027569254651696413757696}\cdot t^{31}-\frac{327436308925677321056070661482031501009178932193023187407841986871272754205504433065}{367312191053078987075006728801024815404055138509303392827515392}\cdot t^{29}+\frac{9172624170635292761088268343119128239022270991648846358983400634191291698626662741445}{734624382106157974150013457602049630808110277018606785655030784}\cdot t^{27}-\frac{202595193177776064810482061291945960611090434717381661527632653783114151947108185282155}{1469248764212315948300026915204099261616220554037213571310061568}\cdot t^{25}+\frac{3503515113744404513682514953241690798866056186857441444231891709555390205693523507133625}{2938497528424631896600053830408198523232441108074427142620123136}\cdot t^{23}-\frac{46967162539282914228537165325081273169099960985083571215453007008186421343621787408278875}{5876995056849263793200107660816397046464882216148854285240246272}\cdot t^{21}+\frac{240817352237233470261080518108019398307539286918342057640279813884708866574686404530296125}{5876995056849263793200107660816397046464882216148854285240246272}\cdot t^{19}-\frac{1856740398550340787592204414966204247648939795113778036854762433541750853755739155889019625}{11753990113698527586400215321632794092929764432297708570480492544}\cdot t^{17}+\frac{42116610256241757962203702323850437178982826588543882906261416564058781201408511564071870875}{94031920909588220691201722573062352743438115458381668563843940352}\cdot t^{15}-\frac{170829067366143724909574776874798516776125015505559465161527695580501543283320396940118105625}{188063841819176441382403445146124705486876230916763337127687880704}\cdot t^{13}+\frac{478443700645597413324555951381348023304569186064074054638290237438917310499473830846786488125}{376127683638352882764806890292249410973752461833526674255375761408}\cdot t^{11}-\frac{884839217779094461151583205591670638725305015574576249854656083853450494439105826414928451875}{752255367276705765529613780584498821947504923667053348510751522816}\cdot t^9+\frac{1019735435000173567567120060098283728257090768966904321912110976940879198724858053717858543125}{1504510734553411531059227561168997643895009847334106697021503045632}\cdot t^7-\frac{673858582897466298140717704369352787723460028257109961088543289073291498794044050963328269375}{3009021469106823062118455122337995287790019694668213394043006091264}\cdot t^5+\frac{218723989830113167227044348670347886187337668236811373747945748063243474216680227475279090625}{6018042938213646124236910244675990575580039389336426788086012182528}\cdot t^3-\frac{22941860727408634407145518307317406655924897303854607634057799027572598365988321418988909375}{12036085876427292248473820489351981151160078778672853576172024365056}\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 (physicists') type can be downloaded here packed into a single file.