Rule: Q[1, 8, 14, 26]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^9-36\cdot t^7+189\cdot t^5-315\cdot t^3+\frac{945}{8}\cdot t$
• $P_3$:
  $2\cdot t^{23}-\frac{3309583}{18099}\cdot t^{21}+\frac{82235713}{12066}\cdot t^{19}-\frac{1089441955}{8044}\cdot t^{17}+\frac{38063466049}{24132}\cdot t^{15}-\frac{179492837615}{16088}\cdot t^{13}+\frac{1547216966295}{32176}\cdot t^{11}-\frac{7941468990455}{64352}\cdot t^9+\frac{46161180640575}{257408}\cdot t^7-\frac{70208873169435}{514816}\cdot t^5+\frac{50216778386775}{1029632}\cdot t^3-\frac{12961617443775}{2059264}\cdot t$
• $P_4$:
  $2\cdot t^{49}-\frac{20994346343936950498403800707026058824760494859858929445816829640473165770414656736973722326951579745280661181037}{26847492324347190683258104751645364380113611833876334765419722350483053209001375079790079692342365588929292102}\cdot t^{47}+\frac{1143744195076654214236760103265847502862219312278473104459821071242581853039967553106305680901001812191169905348429233}{8215332651250240349076980054003481500314765221166158438218435039247814281954420774415764385856763870212363383212}\cdot t^{45}-\frac{82113846553166609412748497710403269367792526017400271721118129192776140401418167982351071824693049853939148519687981755}{5476888434166826899384653369335654333543176814110772292145623359498542854636280516277176257237842580141575588808}\cdot t^{43}+\frac{35962224124982232356820421877076221502571942856999355928466570560061025864896871299947198134441256825541652478360114139021}{32861330605000961396307920216013926001259060884664633752873740156991257127817683097663057543427055480849453532848}\cdot t^{41}-\frac{11337975033432968540114258024301464596206041329053985340177678027022272752971255626641093018537974372580035436526352480814531}{197167983630005768377847521296083556007554365307987802517242440941947542766906098585978345260562332885096721197088}\cdot t^{39}+\frac{296435981083164356445708278227573574031032307327279546035946438703652003475341703088415244799550407378623002263335753788492989}{131445322420003845585231680864055704005036243538658535011494960627965028511270732390652230173708221923397814131392}\cdot t^{37}-\frac{5919322575283403966107212474192726688747886947329883411509170126316375234996858203448390287652783545671700011636430570872706111}{87630214946669230390154453909370469336690829025772356674329973751976685674180488260434820115805481282265209420928}\cdot t^{35}+\frac{824671142364804732598950646306120857270160786728859611354282631577448061078058194711786768386473550609942041117205795233928394535}{525781289680015382340926723456222816020144974154634140045979842511860114045082929562608920694832887693591256525568}\cdot t^{33}-\frac{4994827992012840526803887097043961922506022656350249844866186654191719881384747425303408765145170302661677093350315583602652141375}{175260429893338460780308907818740938673381658051544713348659947503953371348360976520869640231610962564530418841856}\cdot t^{31}+\frac{47597132478042263984967309152762330603466478553737523490598308355477380256667320158842038797565219861112045196871910999128930224865}{116840286595558973853539271879160625782254438701029808899106631669302247565573984347246426821073975043020279227904}\cdot t^{29}-\frac{3217411420615447543809440231647493970980685197566784460084475598206476776224100936710738474379451699233984575251204295465629276415715}{701041719573353843121235631274963754693526632206178853394639790015813485393443906083478560926443850258121675367424}\cdot t^{27}+\frac{2114066654187450609791323855241157728710091928507330429117110526085094910332663705538455659359978803148939656106786620493587507564765}{51929016264692877268239676390738055903224194978235470621825169630800998918032881932109523031588433352453457434624}\cdot t^{25}-\frac{29416036275805506407892898257229914783003941200104355217998430553853388756537854798759870974179417576463648658064123554726760464450125}{103858032529385754536479352781476111806448389956470941243650339261601997836065763864219046063176866704906914869248}\cdot t^{23}+\frac{318850757983765116497309075631008207686466428147908841610249739714412332342631767990210282770048588110884923120105289389963826548873625}{207716065058771509072958705562952223612896779912941882487300678523203995672131527728438092126353733409813829738496}\cdot t^{21}-\frac{2665467255432820263873594786503331672003234676437351683111491457526838762985789059666800220418798244337782669857483833363416068381105625}{415432130117543018145917411125904447225793559825883764974601357046407991344263055456876184252707466819627659476992}\cdot t^{19}+\frac{498495083336450384532419303485513648914925999141413785775007420955116543843842329065891962735468345626534484260329374152748683178894375}{24437184124561354008583377125053202777987856460346103822035373943906352432015473850404481426629850989389862322176}\cdot t^{17}-\frac{9467186302601486795926326189148784613386567781173741233608786625706146152423498584751800737223724466832950155722687838937841945820170625}{195497472996490832068667017000425622223902851682768830576282991551250819456123790803235851413038807915118898577408}\cdot t^{15}+\frac{32742809911466960393632018258254467244403135803077010097500349930394096699241971232210467935599207032396734837288493503028733585793828125}{390994945992981664137334034000851244447805703365537661152565983102501638912247581606471702826077615830237797154816}\cdot t^{13}-\frac{79779796483547503935763109170043481546749990924885439814441715387405927352293864870681625042366184114855537395102320154534375252003268125}{781989891985963328274668068001702488895611406731075322305131966205003277824495163212943405652155231660475594309632}\cdot t^{11}+\frac{130734733531873512122844046379557769357154540501967210516601076351710357886824124153044123531705985234257369786830959512387992480201445625}{1563979783971926656549336136003404977791222813462150644610263932410006555648990326425886811304310463320951188619264}\cdot t^9-\frac{134719215476321992952514769168067402388773071924540825301576284455540702294133764869296528325820365745016839768716081357992715882509513125}{3127959567943853313098672272006809955582445626924301289220527864820013111297980652851773622608620926641902377238528}\cdot t^7+\frac{78674745079800699706859298489814672507510339102104231501021947234636566742817779373846973739139495639187669511233562443941971792509460625}{6255919135887706626197344544013619911164891253848602578441055729640026222595961305703547245217241853283804754477056}\cdot t^5-\frac{21553872588401710738228946401522692571865352665061919994616822027148734401698840062096271251004928953316099559373326267790535504914340625}{12511838271775413252394689088027239822329782507697205156882111459280052445191922611407094490434483706567609508954112}\cdot t^3+\frac{1685186845127382673824269330494937470004866243534082482931040765862865430004991700089068725149736818561694734479541907437747976425034375}{25023676543550826504789378176054479644659565015394410313764222918560104890383845222814188980868967413135219017908224}\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.