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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{58}-\frac{370502600297366783943438132522159499}{229056310072211802412061184914799}\cdot t^{56}+\frac{279028842434932943044799127312720313270}{229056310072211802412061184914799}\cdot t^{54}-\frac{4818948726655784503338999102306341350810}{8483567039711548237483747589437}\cdot t^{52}+\frac{1560830590052600344771890315722157800921275}{8483567039711548237483747589437}\cdot t^{50}-\frac{373424020918607991038291095112292043792013575}{8483567039711548237483747589437}\cdot t^{48}+\frac{68515574887573832750204183820059220155363177700}{8483567039711548237483747589437}\cdot t^{46}-\frac{9880913432419298699527425602938971405793110916500}{8483567039711548237483747589437}\cdot t^{44}+\frac{1138902374478371010580157254736884897357255715362125}{8483567039711548237483747589437}\cdot t^{42}-\frac{106131331036498968544374458654276618085369876870470625}{8483567039711548237483747589437}\cdot t^{40}+\frac{8057998123336234611973282115220517317237858643761240750}{8483567039711548237483747589437}\cdot t^{38}-\frac{500903632305032856661109598922858479267568856801174385750}{8483567039711548237483747589437}\cdot t^{36}+\frac{25558466325025533682016152462581845515280523791885311141875}{8483567039711548237483747589437}\cdot t^{34}-\frac{1071056537401128352339291738518564715962821226119902346529375}{8483567039711548237483747589437}\cdot t^{32}+\frac{36816200552684869953540767803885915227234313757183634745875000}{8483567039711548237483747589437}\cdot t^{30}-\frac{1034905543914448870159052220707452020721788732451745432940855000}{8483567039711548237483747589437}\cdot t^{28}+\frac{23675587546299487588095598886789770309045608395454533951187789375}{8483567039711548237483747589437}\cdot t^{26}-\frac{437823398572149364768950967311408567898538902687611127410180046875}{8483567039711548237483747589437}\cdot t^{24}+\frac{6486387481365966020717845284657567334766333299830951386260081218750}{8483567039711548237483747589437}\cdot t^{22}-\frac{76102133613080171134737905015515103219232694273809522482384199843750}{8483567039711548237483747589437}\cdot t^{20}+\frac{696762784550754176167109064916837933999909695071906042052260416265625}{8483567039711548237483747589437}\cdot t^{18}-\frac{4885474326948511864894944234500057394038935503096243235230773947828125}{8483567039711548237483747589437}\cdot t^{16}+\frac{25606549531317431005719472965383430298090677346504049726154977174062500}{8483567039711548237483747589437}\cdot t^{14}-\frac{97192183148453051743573080459791755277964222137532092835581970542812500}{8483567039711548237483747589437}\cdot t^{12}+\frac{255946615133353214625247676894628417850664438888485708683949401558984375}{8483567039711548237483747589437}\cdot t^{10}-\frac{440306507895228966520204888544693115636469080417764691726087091425421875}{8483567039711548237483747589437}\cdot t^8+\frac{452209809208146927231499647808213162152645414746736269961147203125031250}{8483567039711548237483747589437}\cdot t^6-\frac{239024099524727118663936854845634128079410840066941766445496068431406250}{8483567039711548237483747589437}\cdot t^4+\frac{48604398700103654756984884480484487968242096368363582052695076574765625}{8483567039711548237483747589437}\cdot t^2-\frac{1585839569036258564541296061371091819883118665303830044677275711328125}{8483567039711548237483747589437}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.