Rule: Q[2, 12, 29]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{14}-\frac{248498}{1555}\cdot t^{12}+\frac{3530769}{1555}\cdot t^{10}-\frac{8883963}{622}\cdot t^8+\frac{50229333}{1244}\cdot t^6-\frac{114812775}{2488}\cdot t^4+\frac{78937551}{4976}\cdot t^2-\frac{6151761}{9952}$
• $P_3$:
  $4\cdot t^{43}-\frac{20888293171609213002444876374428885187889963853612865861683762415155608819792212869}{15305977495150692794374540123605900207533615233478761709974758130746142038990240}\cdot t^{41}+\frac{6424745377939860744013626475553747570250101443679952820401616807116750115937448465763}{30611954990301385588749080247211800415067230466957523419949516261492284077980480}\cdot t^{39}-\frac{393897761981906176659546105080849008931945008730461049640586268618130341725362890382401}{20407969993534257059166053498141200276711486977971682279966344174328189385320320}\cdot t^{37}+\frac{920902214707019062877811721527788381932718605098216917060576053234601719909786095894946737}{775502859754301768248310032929365610515036505162923926638721078624471196642172160}\cdot t^{35}-\frac{730544909197712473498117178141333092979094626780149701450219271977770028336851108769688809}{14100051995532759422696546053261192918455209184780435029794928702263112666221312}\cdot t^{33}+\frac{794961308695682323048955898420073741568897665041473286116651144397785688411345030268182413637}{479401767848113820371682565810880559227477112282534791013027575876945830651524608}\cdot t^{31}-\frac{38086749190576178936379992218326190871801131473200948387972887517726854671178011807360653233041}{958803535696227640743365131621761118454954224565069582026055151753891661303049216}\cdot t^{29}+\frac{1381427120614593238356749520152991431201959072569799255476727795687949506563451654630587526620951}{1917607071392455281486730263243522236909908449130139164052110303507783322606098432}\cdot t^{27}-\frac{19061622976807417625632546419899380013755783863179760313442445351048798258534829822149289858353549}{1917607071392455281486730263243522236909908449130139164052110303507783322606098432}\cdot t^{25}+\frac{400180122425994306530548700543832593943573310731720770087545928326842245557468980617663530546076325}{3835214142784910562973460526487044473819816898260278328104220607015566645212196864}\cdot t^{23}-\frac{6360072654013990121527443538546367321970912870177293288287043676404307304057671074027829484956294375}{7670428285569821125946921052974088947639633796520556656208441214031133290424393728}\cdot t^{21}+\frac{75788290759797916378479177017151009905862660423280347285851107796936939289306885610725336733900202175}{15340856571139642251893842105948177895279267593041113312416882428062266580848787456}\cdot t^{19}-\frac{70230054615679089046592173214262544321164720928086555017007125091123737863484136070105203329891987775}{3229654014976766789872387811778563767427214230113918592087764721697319280178692096}\cdot t^{17}+\frac{26310165941392598172450304251945044675158110087573379210654998747829045005158867248769598341863740225}{379959295879619622337927977856301619697319321189872775539737026082037562373963776}\cdot t^{15}-\frac{117780699458423437600116837174419157187181168440171298975519328727717447109405054053349133162693556125}{759918591759239244675855955712603239394638642379745551079474052164075124747927552}\cdot t^{13}+\frac{356266195026598698354043423460127788482640948868205016031396989826561518958134033754293539352010952875}{1519837183518478489351711911425206478789277284759491102158948104328150249495855104}\cdot t^{11}-\frac{1378204731257949605948913509266197779515247574994886451254373236033655475774405782830516878463810029875}{6079348734073913957406847645700825915157109139037964408635792417312600997983420416}\cdot t^9+\frac{1573903161051848024798514244707540271721649126775496168043444174470149568969338123293902808925829146125}{12158697468147827914813695291401651830314218278075928817271584834625201995966840832}\cdot t^7-\frac{938125640103756693976481797773148574253781894399659593538324166525927612618622383460722171594412767125}{24317394936295655829627390582803303660628436556151857634543169669250403991933681664}\cdot t^5+\frac{234721513920989188232860963601600739203840680735451102659625659072362999844147993845168067552965699375}{48634789872591311659254781165606607321256873112303715269086339338500807983867363328}\cdot t^3-\frac{3621946873720865440233249344145277261962350051959447637943940549849537352479975346647231041007126875}{24317394936295655829627390582803303660628436556151857634543169669250403991933681664}\cdot t$

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.