Rule: Q[4, 7, 42]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{11}-328\cdot t^9+2112\cdot t^7-5040\cdot t^5+4095\cdot t^3-\frac{1575}{2}\cdot t$
• $P_3$:
  $16\cdot t^{53}-\frac{63069332325501366950894327604172116588931432837956046688641135588015229195804}{6086473267365702129997460815765956775861662767203642168363652970518867201}\cdot t^{51}+\frac{691584205402015640632614651548685408105412888093277908341786213945581084757717570}{225199510892530978809906050183340400706881522386534760229455159909198086437}\cdot t^{49}-\frac{124748232133183720738742733067639866409745994106948604145051049179175820612771227314}{225199510892530978809906050183340400706881522386534760229455159909198086437}\cdot t^{47}+\frac{15363094522379800363025724339352992881157304878289759464920368630977069822354959033235}{225199510892530978809906050183340400706881522386534760229455159909198086437}\cdot t^{45}-\frac{1373269656610777920714164867249667074161974982434245762074108405334733815208706644412530}{225199510892530978809906050183340400706881522386534760229455159909198086437}\cdot t^{43}+\frac{184919251097657171769046176243699730538408242291271049273426182563628021663515509518565735}{450399021785061957619812100366680801413763044773069520458910319818396172874}\cdot t^{41}-\frac{38419260470448634277199514212340951805874203529857887322265027440125980776863115530599421875}{1801596087140247830479248401466723205655052179092278081835641279273584691496}\cdot t^{39}+\frac{2224881147715211985500395836856093932859048024971369198497007083692670016404120044481073465}{2562725586259243002104194027690929168783858007243638807732064408639523032}\cdot t^{37}-\frac{573929144964966403140732628991280119305534435707039647716409588853992675636997577320947449125}{20501804690073944016833552221527433350270864057949110461856515269116184256}\cdot t^{35}+\frac{29507184643949478593601088125910514219904822933918704413658527166418048622568738486289559177275}{41003609380147888033667104443054866700541728115898220923713030538232368512}\cdot t^{33}-\frac{303394147650032202383716714971034363869099139552137269931612100986326806083442991874620334534075}{20501804690073944016833552221527433350270864057949110461856515269116184256}\cdot t^{31}+\frac{9990509566571535069772207927777847457106908362651259698827978831841887314516060954739989590137125}{41003609380147888033667104443054866700541728115898220923713030538232368512}\cdot t^{29}-\frac{131504876485343772463587584664990534521510351014831067060368819690570721103151308684987616521165075}{41003609380147888033667104443054866700541728115898220923713030538232368512}\cdot t^{27}+\frac{689376779883478396247057634161724350609957023131870386623673589634088298594003596020020588407430375}{20501804690073944016833552221527433350270864057949110461856515269116184256}\cdot t^{25}-\frac{91555105694073396977527671084286950460836531781180710754535387061995682918401086923423149802123793125}{328028875041183104269336835544438933604333824927185767389704244305858948096}\cdot t^{23}+\frac{2385863160057886703553802456629312463917108649839639423064829682212715313829651923772578683209402169375}{1312115500164732417077347342177755734417335299708743069558816977223435792384}\cdot t^{21}-\frac{48227230054961722719503346358058833304230386585118466834553445495294945566136990076466750361234951284375}{5248462000658929668309389368711022937669341198834972278235267908893743169536}\cdot t^{19}+\frac{372209852058176776776775450786136361523226364255206909916742824722562035559939855340148901447464700493125}{10496924001317859336618778737422045875338682397669944556470535817787486339072}\cdot t^{17}-\frac{1074263969982152291758628224950542755917583329342234627127495841087224264317580559259049815560619510721875}{10496924001317859336618778737422045875338682397669944556470535817787486339072}\cdot t^{15}+\frac{4511186473705371948525056930663075034737519006485668680390828153771449799361194357539995267765551303465625}{20993848002635718673237557474844091750677364795339889112941071635574972678144}\cdot t^{13}-\frac{1659384579646606182934110416853563414445293135390916039707240427066421064571066490872304064128546967409375}{5248462000658929668309389368711022937669341198834972278235267908893743169536}\cdot t^{11}+\frac{12998016847816959239743437287491040990981069643979086188824883685221697864338607366696076240166748745359375}{41987696005271437346475114949688183501354729590679778225882143271149945356288}\cdot t^9-\frac{31469298621941054344308140001781725247221874412162703326519750530756819627235062541118762304502152432565625}{167950784021085749385900459798752734005418918362719112903528573084599781425152}\cdot t^7+\frac{5267072055183813116704136126965932384718740239849806745304548657838141772401790838482291093302106746140625}{83975392010542874692950229899376367002709459181359556451764286542299890712576}\cdot t^5-\frac{12918673252209893224754169300657155335519160085431261363622093361927833713060258528914584046427006499234375}{1343606272168685995087203678390021872043351346901752903228228584676798251401216}\cdot t^3+\frac{1188482173252745613881830180639479086036271425257587123484695822918877507087761617344111972337554040390625}{2687212544337371990174407356780043744086702693803505806456457169353596502802432}\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.