Rule: Q[4, 15, 28]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{19}-\frac{748536}{667}\cdot t^{17}+\frac{226304664}{7337}\cdot t^{15}-\frac{3155515020}{7337}\cdot t^{13}+\frac{24226003620}{7337}\cdot t^{11}-\frac{9496214910}{667}\cdot t^9+\frac{1965071745}{58}\cdot t^7-\frac{112008278655}{2668}\cdot t^5+\frac{250467132825}{10672}\cdot t^3-\frac{83438061525}{21344}\cdot t$
• $P_3$:
  $16\cdot t^{47}-\frac{94932843271577860536816831937884374924758489807924975718694466041829082469880363737466213619435339112}{14754889366344037615700338574737211355293216469316160972180519915290685398042078456273183160004613}\cdot t^{45}+\frac{3636560291880333784589999564173884250210037011272095120051451442492443619477530036664562607709170138662736}{3083771877565903861681370762120077173256282242087077643185728662295753248190794397361095280440964117}\cdot t^{43}-\frac{403519736826478926550391447566258040088697261730752656257229063961047915738419282948235912922433376869278152}{3083771877565903861681370762120077173256282242087077643185728662295753248190794397361095280440964117}\cdot t^{41}+\frac{2581293196915339056044739773280580240902681928897981018703829281073465235498138580127778376358686244927032559747}{262120609593101828242916514780206559726783990577401599670786936295139026096217523775693098837481949945}\cdot t^{39}-\frac{12164494761016507090641731502623072010122583985859303602746780191233368092868730872783074220547964199768499484289}{22793096486356680716775349111322309541459477441513182580068429243055567486627610763103747724998430430}\cdot t^{37}+\frac{11315493584872569462014679900243364528047789940972694819308609664567854774772622424203565028507626843379750140556763}{524241219186203656485833029560413119453567981154803199341573872590278052192435047551386197674963899890}\cdot t^{35}-\frac{139705554458983526859491207968476335310795663457705221436392778602456129474297242350054618367289014609317101308894349}{209696487674481462594333211824165247781427192461921279736629549036111220876974019020554479069985559956}\cdot t^{33}+\frac{606857505887720008311126076310539764538418046598232481432185936092840171297790583871957451576106974523925926951518313}{38126634122632993198969674877120954142077671356712959952114463461111131068540730731009905285451919992}\cdot t^{31}-\frac{22632230798777927505645240239117288819558322897711130748460231560474034746523454581461516938472705147618143874725406577}{76253268245265986397939349754241908284155342713425919904228926922222262137081461462019810570903839984}\cdot t^{29}+\frac{11402870015143964615568100107657756397784823245747847501121707433785425613588815290982529713510875563369165763373058129}{2629423042940206427515149991525583044281218714256066203594100928352491797830395222828269330031166896}\cdot t^{27}-\frac{261150605504618511933022192730612109333143084126697219005022109551683588773976257523468848637270124066780698055564712317}{5258846085880412855030299983051166088562437428512132407188201856704983595660790445656538660062333792}\cdot t^{25}+\frac{406294943604888418303159200507445561568131458882561303556502480909067764084303254386574702737071547079056466855682257425}{914581927979202235657443475313246276271728248436892592554469888122605842723615729679398027836927616}\cdot t^{23}-\frac{5641468406399544596148144459189846733055134142857288018501146397021555216767464691166711809358977411039756386713820470725}{1829163855958404471314886950626492552543456496873785185108939776245211685447231459358796055673855232}\cdot t^{21}+\frac{395851406317132883335620903461931121511807159676467271269458022018725309484765124334053167945009731059317622765672985875}{24067945473136900938353775666138059901887585485181384014591312845331732703253045517878895469392832}\cdot t^{19}-\frac{376006744882606218785537038036533762756837417512819981016942302808615379091458386132402501803405803753242607957116670125}{5663045993679270809024417803797190565150020114160325650492073610666290047824246004206798933974784}\cdot t^{17}+\frac{18022516655210669951330109398412552871866798892271721356473260593834872351320131498477830521365131057843379164533452391375}{90608735898868332944390684860755049042400321826565210407873177770660640765187936067308782943596544}\cdot t^{15}-\frac{77999337704345324190501741330068380552148430734547654087801644279610505749458475984447090640144257640714923887710807854375}{181217471797736665888781369721510098084800643653130420815746355541321281530375872134617565887193088}\cdot t^{13}+\frac{14691352913887472570985208391830761106365427644769193761775773887771896674824657783751743327754134554360956479651175756875}{22652183974717083236097671215188762260600080456641302601968294442665160191296984016827195735899136}\cdot t^{11}-\frac{29301438927436612985835956918512151852674148898608340604193732011068763053418551430459279207000138020286234941201221893875}{45304367949434166472195342430377524521200160913282605203936588885330320382593968033654391471798272}\cdot t^9+\frac{575572768197928025319726407988411201588964327447776593133407586587772657705336521022110586434553759762784689447551974585125}{1449739774381893327110250957772080784678405149225043366525970844330570252243006977076940527097544704}\cdot t^7-\frac{390485071174229944782350442403708885168390392726693491194042322275163018241707301540380945269098783390893073768818366426625}{2899479548763786654220501915544161569356810298450086733051941688661140504486013954153881054195089408}\cdot t^5+\frac{61377059974335649538786716424772026272267550598300523016735845723055455102056334996985533278099176734601947882725129256875}{2899479548763786654220501915544161569356810298450086733051941688661140504486013954153881054195089408}\cdot t^3-\frac{6085504241581199406127636527446717241699389593565109704127320270593620837109964962976850129974421175561173350318346223125}{5798959097527573308441003831088323138713620596900173466103883377322281008972027908307762108390178816}\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.