Rule: Q[2, 56]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{58}-\frac{741005200594733567886876265044318998}{229056310072211802412061184914799}\cdot t^{56}+\frac{279028842434932943044799127312720313270}{229056310072211802412061184914799}\cdot t^{54}-\frac{2409474363327892251669499551153170675405}{8483567039711548237483747589437}\cdot t^{52}+\frac{1560830590052600344771890315722157800921275}{33934268158846192949934990357748}\cdot t^{50}-\frac{373424020918607991038291095112292043792013575}{67868536317692385899869980715496}\cdot t^{48}+\frac{17128893721893458187551045955014805038840794425}{33934268158846192949934990357748}\cdot t^{46}-\frac{2470228358104824674881856400734742851448277729125}{67868536317692385899869980715496}\cdot t^{44}+\frac{1138902374478371010580157254736884897357255715362125}{542948290541539087198959845723968}\cdot t^{42}-\frac{106131331036498968544374458654276618085369876870470625}{1085896581083078174397919691447936}\cdot t^{40}+\frac{4028999061668117305986641057610258658618929321880620375}{1085896581083078174397919691447936}\cdot t^{38}-\frac{250451816152516428330554799461429239633784428400587192875}{2171793162166156348795839382895872}\cdot t^{36}+\frac{25558466325025533682016152462581845515280523791885311141875}{8687172648664625395183357531583488}\cdot t^{34}-\frac{1071056537401128352339291738518564715962821226119902346529375}{17374345297329250790366715063166976}\cdot t^{32}+\frac{4602025069085608744192595975485739403404289219647954343234375}{4343586324332312697591678765791744}\cdot t^{30}-\frac{129363192989306108769881527588431502590223591556468179117606875}{8687172648664625395183357531583488}\cdot t^{28}+\frac{23675587546299487588095598886789770309045608395454533951187789375}{138994762378634006322933720505335808}\cdot t^{26}-\frac{437823398572149364768950967311408567898538902687611127410180046875}{277989524757268012645867441010671616}\cdot t^{24}+\frac{3243193740682983010358922642328783667383166649915475693130040609375}{277989524757268012645867441010671616}\cdot t^{22}-\frac{38051066806540085567368952507757551609616347136904761241192099921875}{555979049514536025291734882021343232}\cdot t^{20}+\frac{696762784550754176167109064916837933999909695071906042052260416265625}{2223916198058144101166939528085372928}\cdot t^{18}-\frac{4885474326948511864894944234500057394038935503096243235230773947828125}{4447832396116288202333879056170745856}\cdot t^{16}+\frac{6401637382829357751429868241345857574522669336626012431538744293515625}{2223916198058144101166939528085372928}\cdot t^{14}-\frac{24298045787113262935893270114947938819491055534383023208895492635703125}{4447832396116288202333879056170745856}\cdot t^{12}+\frac{255946615133353214625247676894628417850664438888485708683949401558984375}{35582659168930305618671032449365966848}\cdot t^{10}-\frac{440306507895228966520204888544693115636469080417764691726087091425421875}{71165318337860611237342064898731933696}\cdot t^8+\frac{226104904604073463615749823904106581076322707373368134980573601562515625}{71165318337860611237342064898731933696}\cdot t^6-\frac{119512049762363559331968427422817064039705420033470883222748034215703125}{142330636675721222474684129797463867392}\cdot t^4+\frac{48604398700103654756984884480484487968242096368363582052695076574765625}{569322546702884889898736519189855469568}\cdot t^2-\frac{1585839569036258564541296061371091819883118665303830044677275711328125}{1138645093405769779797473038379710939136}$

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.