Rule: Q[8, 52]

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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{60}-\frac{1473581004404202414899914318723652556988991685672352073434272298240}{7325079701492144457860066035142819399915536933854848280742289}\cdot t^{58}+\frac{12398302016446704198343457930783408141744702390346348776704317353239488}{168476833134319322530781518808284846198057349478661510457072647}\cdot t^{56}-\frac{2808001636188806674245154430787337556027086820325444260691798269458821760}{168476833134319322530781518808284846198057349478661510457072647}\cdot t^{54}+\frac{4859283159160525182261144551865270664114056132884555267265754675544185357840}{1853245164477512547838596706891133308178630844265276615027799117}\cdot t^{52}-\frac{564759965997788725762871002504244174864750114207240233510946976716180510934960}{1853245164477512547838596706891133308178630844265276615027799117}\cdot t^{50}+\frac{50353802796829691088713380927183131638015982972287196175232126354206538974666500}{1853245164477512547838596706891133308178630844265276615027799117}\cdot t^{48}-\frac{75118328827304828001111344087476593569768602455437182393986559750110102934981200}{39430748180372607400821206529598581025077252005644183298463811}\cdot t^{46}+\frac{183164117362646837566659851854300700934107034239798733411838900268044207710332625}{1714380355668374234818313327373851348916402261114964491237557}\cdot t^{44}-\frac{755786176455459458775295346290590978045511654885230700942541295216146576928889875}{155852759606215839528937575215804668083309296464996771930687}\cdot t^{42}+\frac{111959464735239724879696508359054585594091757196807886908738660221099309891410176875}{623411038424863358115750300863218672333237185859987087722748}\cdot t^{40}-\frac{1700597362307049249246911085796104821484977168007031790429909917707200834899415791875}{311705519212431679057875150431609336166618592929993543861374}\cdot t^{38}+\frac{340086319794443832287674309310733438936957841327502074730424141594617959356974881731375}{2493644153699453432463001203452874689332948743439948350890992}\cdot t^{36}-\frac{7004273650877085970956366243898870724517835309156414051064645180319560951793640358645625}{2493644153699453432463001203452874689332948743439948350890992}\cdot t^{34}+\frac{475228416854933251091486505357214673468134916964991862723299167741735588243246126934989375}{9974576614797813729852004813811498757331794973759793403563968}\cdot t^{32}-\frac{828225146537016529099452647096889712772530365407135157076908154399041151085293644042279375}{1246822076849726716231500601726437344666474371719974175445496}\cdot t^{30}+\frac{302669267545397513385187093305640352725708143339084463363717577363684431751588620690382578125}{39898306459191254919408019255245995029327179895039173614255872}\cdot t^{28}-\frac{2816708941253275464591540395278386205238571868289369512166662584901535692964613645951139805625}{39898306459191254919408019255245995029327179895039173614255872}\cdot t^{26}+\frac{84853117487165995289771516358200351370425468928060151446441567562667102692114783487934025453125}{159593225836765019677632077020983980117308719580156694457023488}\cdot t^{24}-\frac{256259533792049486401549152839623053639086560161599510729858290374232067584908145257893555671875}{79796612918382509838816038510491990058654359790078347228511744}\cdot t^{22}+\frac{9817043081187371480996957239025888481469113174899073256896718755166141116900962431899872055890625}{638372903347060078710528308083935920469234878320626777828093952}\cdot t^{20}-\frac{36726635151161669212731227963253830394845828214628019581088467010334069678061898621297074489921875}{638372903347060078710528308083935920469234878320626777828093952}\cdot t^{18}+\frac{421375745228031192504512129171797388191384912544280244703762160436519523408875218758208711141890625}{2553491613388240314842113232335743681876939513282507111312375808}\cdot t^{16}-\frac{226100341270559575766066379368071454768090435794543431665553336201935970642220870266932617901015625}{638372903347060078710528308083935920469234878320626777828093952}\cdot t^{14}+\frac{5626614761059941758480048865013894378912319708868391855931952237199398507946560270796042668965390625}{10213966453552961259368452929342974727507758053130028445249503232}\cdot t^{12}-\frac{6072201530082497837665135428754728208127536196690121308510948754764177949021252272059803999466265625}{10213966453552961259368452929342974727507758053130028445249503232}\cdot t^{10}+\frac{17109300873389728060545719601904215555991158014284945842641828315980802073353672654918555277026015625}{40855865814211845037473811717371898910031032212520113780998012928}\cdot t^8-\frac{3590505489056996545729446091320405639183224317947797038426199024707611003614626144449798707654578125}{20427932907105922518736905858685949455015516106260056890499006464}\cdot t^6+\frac{6186136961756321005682642729949457955223740295102790141549654489435140960378190292219997899378203125}{163423463256847380149895246869487595640124128850080455123992051712}\cdot t^4-\frac{510966722017059019889951667810344058796231377953931104363416489288951206587059258802623064553046875}{163423463256847380149895246869487595640124128850080455123992051712}\cdot t^2+\frac{27077472360149925476280981184928082352346914965155478086889387508274663917451207444473888069453125}{653693853027389520599580987477950382560496515400321820495968206848}$

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.