Rule: Q[10, 48]

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.

• $P_1$:
  $1024\cdot t^{10}-23040\cdot t^8+161280\cdot t^6-403200\cdot t^4+302400\cdot t^2-30240$
• $P_2$:
  $1024\cdot t^{58}-\frac{149496274263206082738559540170171492768036671196387238005746176}{209168570909958037457951997454585046444810463382949369601}\cdot t^{56}+\frac{660718690270808957699960975569147874963473408578090725183662620160}{2858637135769426511925343965212662301412409666233641384547}\cdot t^{54}-\frac{131614944199280989972922116221818874686838332487223236889170262065920}{2858637135769426511925343965212662301412409666233641384547}\cdot t^{52}+\frac{33635460204122851639360270599181947690621524910283171245490473129506240}{5308897537857506379289924506823515702623046523005333999873}\cdot t^{50}-\frac{21527696651902191096295419843440860800715668165902685666034824397370228320}{33623017739764207068836188543215599449945961312367115332529}\cdot t^{48}+\frac{1658173612075661340296166726857637327163896048969531174086210473072644124480}{33623017739764207068836188543215599449945961312367115332529}\cdot t^{46}-\frac{99733880473163964420187048607094838618237756342745096106121528254797791015200}{33623017739764207068836188543215599449945961312367115332529}\cdot t^{44}+\frac{4761254908675217129439091732332335166970253942178009190055616665898967685789700}{33623017739764207068836188543215599449945961312367115332529}\cdot t^{42}-\frac{4449207020508630405609414798083562008690523683909042263436363288516229201850650}{820073603408883099239907037639404864632828324691880861769}\cdot t^{40}+\frac{10600185674983460116285627504880828491790939726457330375846738212058679097019150}{63082584877606392249223618279954220356371409591683143213}\cdot t^{38}-\frac{14030572376905659247275543227967001564240208435628658548336233679688013392526025}{3320136046189810118380190435787064229282705767983323327}\cdot t^{36}+\frac{1148392446815774907364759144569882676024385843975782599657599480458373120296892625}{13280544184759240473520761743148256917130823071933293308}\cdot t^{34}-\frac{38242134340024217119481529637729237812025993200008944179500844494720798181062377125}{26561088369518480947041523486296513834261646143866586616}\cdot t^{32}+\frac{129302691442269686009289520564765161139754648824540136819067356462943585098135530125}{6640272092379620236760380871574128458565411535966646654}\cdot t^{30}-\frac{2831037707845516465205760534191125750447327514817450482935500136591397373126921377625}{13280544184759240473520761743148256917130823071933293308}\cdot t^{28}+\frac{399273994295749409461679502958477748788083359705870532659066478687621043394803117711125}{212488706956147847576332187890372110674093169150932692928}\cdot t^{26}-\frac{5627423754687622656353684422171660880561472208743994499204342129554927123916726452565625}{424977413912295695152664375780744221348186338301865385856}\cdot t^{24}+\frac{31414738687596808234057431123029261656634245652808311074006716334521587275834752545503125}{424977413912295695152664375780744221348186338301865385856}\cdot t^{22}-\frac{274653958948071132905747344562762797213037181019059825367782504485328136001661550970090625}{849954827824591390305328751561488442696372676603730771712}\cdot t^{20}+\frac{3706980548267876526796613986948310499918370722644868951700577154011903757272290565525821875}{3399819311298365561221315006245953770785490706414923086848}\cdot t^{18}-\frac{18967091265305331656793662829732165888005128285690400765600505846781147645312164219358059375}{6799638622596731122442630012491907541570981412829846173696}\cdot t^{16}+\frac{17985730292603312694595515580001780800958723707151196576407830540067493010261492677446671875}{3399819311298365561221315006245953770785490706414923086848}\cdot t^{14}-\frac{49134183914946900596153267454740927014894289183015834212598332645816247380971743156034984375}{6799638622596731122442630012491907541570981412829846173696}\cdot t^{12}+\frac{372053472143465403407176870895889427230018175457080938972900237959632238673560172498222328125}{54397108980773848979541040099935260332567851302638769389568}\cdot t^{10}-\frac{461783621854784646507850495443338180654118381804857705561848666309219936597227069399156890625}{108794217961547697959082080199870520665135702605277538779136}\cdot t^8+\frac{172048966984013110347706945759826622025216046831993718048766221675521659329942335286329671875}{108794217961547697959082080199870520665135702605277538779136}\cdot t^6-\frac{65564810352041958333336789008016924676251589427982604720889447040682422867452242781358984375}{217588435923095395918164160399741041330271405210555077558272}\cdot t^4+\frac{18029920884054293450768562688319602816641133107144965589950194819690102104663749561374921875}{870353743692381583672656641598964165321085620842220310233088}\cdot t^2-\frac{288019055560707364851459291010561003894211814624496932806444783286946105094567050033359375}{1740707487384763167345313283197928330642171241684440620466176}$

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.