Rule: Q[4, 65]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{69}-\frac{65234713701654832486118597685054184375923122439080325290153174}{29435603524201073832079503952842058087131298266682789732649}\cdot t^{67}+\frac{4149016717239237586805616842358795647811006209922491439085075124127}{1795571814976265503756849741123365543315009194267650173691589}\cdot t^{65}-\frac{2708482006942586440698634332935966852410807400281773452038006533153120}{1795571814976265503756849741123365543315009194267650173691589}\cdot t^{63}+\frac{40092547222520939440063210056110236593391682084040341999425785693909240}{57921671450847274314737088423334372365000296589279037861019}\cdot t^{61}-\frac{225654776350668500670578963133985946867163506406965021425743412474257840}{949535597554873349421919482349743809262299944086541604279}\cdot t^{59}+\frac{60241466518387475228392818405652801841458416118422801775554140961935019240}{949535597554873349421919482349743809262299944086541604279}\cdot t^{57}-\frac{12830719764156937969505757462899073756304688360737850862014071246689210234720}{949535597554873349421919482349743809262299944086541604279}\cdot t^{55}+\frac{2219818548419049370238873390256270200950891474427363222864239659227216258862900}{949535597554873349421919482349743809262299944086541604279}\cdot t^{53}-\frac{316008784854491391181980056992577622623052347111878660131259216248153064171483800}{949535597554873349421919482349743809262299944086541604279}\cdot t^{51}+\frac{37364486416054615850459229134086064584166328139714192439194675930822255684187629500}{949535597554873349421919482349743809262299944086541604279}\cdot t^{49}-\frac{3694206945595702243201220202544989787051224627762101333352465520282939949701542132000}{949535597554873349421919482349743809262299944086541604279}\cdot t^{47}+\frac{306850680868347141723249529727213645758909803927071006701723258421101125433289097141000}{949535597554873349421919482349743809262299944086541604279}\cdot t^{45}-\frac{21478415075168024266316009583848594518880132223774913391931216216240061337271345646530000}{949535597554873349421919482349743809262299944086541604279}\cdot t^{43}+\frac{29511955001325075089142241291585293463391409164909346293412185905999077886265958795345000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{41}-\frac{1472434994256164573189696662135941858098470720827244430323434231590715943046128436921460000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{39}+\frac{61992726840486556971104207721462240491494837451470766073056023532294262957265040175334728750}{22082223198950543009812080984877763006099998699687014053}\cdot t^{37}-\frac{2198530076314390816404796374364177291159943815529550054776187313099925377074671157229105792500}{22082223198950543009812080984877763006099998699687014053}\cdot t^{35}+\frac{65487984103797914019692062324629639188195443917230180432912749092568538223056226433272262106250}{22082223198950543009812080984877763006099998699687014053}\cdot t^{33}-\frac{1631898891002393729199963243796423529864812370504369260408705973639894581123727618319692526900000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{31}+\frac{33843370862835229552312333594894180732119704543731494426366100935156572985191375157137920629675000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{29}-\frac{580334392120293355564682561816927460143904112308113260816819123450622684585609516166057476588550000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{27}+\frac{8162763747978475891422538685305804927258814750422686726568310672437987346619380372292048329736525000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{25}-\frac{93267632691172158003716390165164280701016832984910660962876479249035957876921515334834740893977500000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{23}+\frac{855557410531091740425756001270560460366085904974364844158437455939895901686829394982967334021853437500}{22082223198950543009812080984877763006099998699687014053}\cdot t^{21}-\frac{6211492249888767739634824366170437123984174159650680157190886003844849897849284534869243719711270125000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{19}+\frac{35076564935527719141929650187336957899352919157093554154781139517272057846847583415505906953790874812500}{22082223198950543009812080984877763006099998699687014053}\cdot t^{17}-\frac{150800985635400969982357418744865934881633805725133805298166686147885387918936009237336078371937868500000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{15}+\frac{480497535659666563451936272163872303524364223800852506515234818021583688794353801950118867687461800625000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{13}-\frac{1096138992677303364046349563692047556475202232311922143567858363599838638162110843083130201588820826250000}{22082223198950543009812080984877763006099998699687014053}\cdot t^{11}+\frac{1709232933828162103363836567328093952624780426320305506730329569300634467779597703057922239394741079375000}{22082223198950543009812080984877763006099998699687014053}\cdot t^9-\frac{1705104300748266140191284608733557073285459512154536821193746752429840403417344735743371264868045857500000}{22082223198950543009812080984877763006099998699687014053}\cdot t^7+\frac{980622025493784862835320565961388904080776929765808078137148826886104523631685793230498891877143605703125}{22082223198950543009812080984877763006099998699687014053}\cdot t^5-\frac{268952390787582639952161415061246164040268731073859173946999222784961025200146174016052613306912899218750}{22082223198950543009812080984877763006099998699687014053}\cdot t^3+\frac{22452868708068534800025851222020511794115306234898298838830003507884581372433749355588545151782405859375}{22082223198950543009812080984877763006099998699687014053}\cdot t$

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.