Rule: Q[3, 72]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{75}-\frac{6198343405440649591171005557652828559327116}{570831318897806310999477864496173894245}\cdot t^{73}+\frac{3981721675422981478572809080344569368395318924}{570831318897806310999477864496173894245}\cdot t^{71}-\frac{46045058846078898079664165526849559417533884526}{16309466254223037457127938985604968407}\cdot t^{69}+\frac{26376710168596200240781127943133135637761634386707}{32618932508446074914255877971209936814}\cdot t^{67}-\frac{11385762647858263452316504324268853868231151239620213}{65237865016892149828511755942419873628}\cdot t^{65}+\frac{481335575897075776853582401123650190155911335982338926}{16309466254223037457127938985604968407}\cdot t^{63}-\frac{65465690468980939172896221273293181420041953495568372769}{16309466254223037457127938985604968407}\cdot t^{61}+\frac{58363337311792623839366693294701002601700862193764425805315}{130475730033784299657023511884839747256}\cdot t^{59}-\frac{183104607498840329081162997733980397990870752359269991698095}{4422906102840145751085542775757279568}\cdot t^{57}+\frac{14216335889375973178124458702499153717025623711116197986275965}{4422906102840145751085542775757279568}\cdot t^{55}-\frac{1865824753546505892902234875086600676041267786834957835730933115}{8845812205680291502171085551514559136}\cdot t^{53}+\frac{416258009212259658418677710552125649531909540256366247314588982665}{35383248822721166008684342206058236544}\cdot t^{51}-\frac{39622906925692810836810094970052812564968083690291338646483955107375}{70766497645442332017368684412116473088}\cdot t^{49}+\frac{806830691136155566364478165662743953404284288810374202240932267520875}{35383248822721166008684342206058236544}\cdot t^{47}-\frac{56325889607747722378238388549845568614848144303648356442070886499174125}{70766497645442332017368684412116473088}\cdot t^{45}+\frac{26980559466770167635535975060660047878908629425879393961109400854910209875}{1132263962327077312277898950593863569408}\cdot t^{43}-\frac{1385297801803988650737710873741136763647122762445407346441442514243205457125}{2264527924654154624555797901187727138816}\cdot t^{41}+\frac{30464179169167590286206554030206787447818789007011929356771814281166264935625}{2264527924654154624555797901187727138816}\cdot t^{39}-\frac{1145599761259195457585444721516086262556671488574593630406053413778254483899375}{4529055849308309249111595802375454277632}\cdot t^{37}+\frac{73466229225728935940988333467883580455584119711323086258807204301362240711604375}{18116223397233236996446383209501817110528}\cdot t^{35}-\frac{2001339573295204541525604707012548115038661018034716707422852118610960762539460625}{36232446794466473992892766419003634221056}\cdot t^{33}+\frac{5763407955584267694169619897305184351507315932745837912538500346049974114750391875}{9058111698616618498223191604750908555264}\cdot t^{31}-\frac{111656551910719940006501214704839862018385725969356497904605505059312420129361603125}{18116223397233236996446383209501817110528}\cdot t^{29}+\frac{7226260692390229721587928589966257314016707559859530546074412551861914095740803028125}{144929787177865895971571065676014536884224}\cdot t^{27}-\frac{96835209665057278778412620788066442865641973180928170464478090429733376188703051596875}{289859574355731791943142131352029073768448}\cdot t^{25}+\frac{532002226205513839994600331767345959860515608969779992665796703642262375806953242378125}{289859574355731791943142131352029073768448}\cdot t^{23}-\frac{4735220913348741238359263541059945785147906651552993610234014104429091438397430268696875}{579719148711463583886284262704058147536896}\cdot t^{21}+\frac{67280758939353902973759081822276969196264727841392953782327886454265864774612257882203125}{2318876594845854335545137050816232590147584}\cdot t^{19}-\frac{374626824638603915194279137944826294007522633121481433907099689293045041842344260569171875}{4637753189691708671090274101632465180295168}\cdot t^{17}+\frac{399533064038992332038716273922389830891668396374370982039478454529635729555755418983078125}{2318876594845854335545137050816232590147584}\cdot t^{15}-\frac{1268430687619178187742296777686049532269521609585858567527277820172617523466763579958546875}{4637753189691708671090274101632465180295168}\cdot t^{13}+\frac{46160564691080621234268724733312303597623263510501833704170757996081640619735996632389078125}{148408102070134677474888771252238885769445376}\cdot t^{11}-\frac{71420554275022155244313125228114459061225307078591972124629468342385329707113689410658046875}{296816204140269354949777542504477771538890752}\cdot t^9+\frac{34891853328481733875506199006257394655159210279831058392986415307159489731294497641529921875}{296816204140269354949777542504477771538890752}\cdot t^7-\frac{19183694989171043102413857852696045413801837146126878926113161365716047652940813474685703125}{593632408280538709899555085008955543077781504}\cdot t^5+\frac{9684598878473914377513331278687585574726748957975068231352485303964667481724960202474140625}{2374529633122154839598220340035822172311126016}\cdot t^3-\frac{706345088888966155704240304080146966451101761377629130934945303088142129786893840280234375}{4749059266244309679196440680071644344622252032}\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.