Rule: Q[4, 5, 38]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^9-168\cdot t^7+432\cdot t^5-270\cdot t^3+45\cdot t$
• $P_3$:
  $16\cdot t^{47}-\frac{1210416446467091249886306809359296099379668383310420190068827328}{157281009354020553361820686714156147142188786633746890875247}\cdot t^{45}+\frac{644948692286679587164282900115025437322952400269161771830862525096}{381968165574049915307278810591522071631029910396242449268457}\cdot t^{43}-\frac{599805336707917101998550398985104093884576320067771173306090300221754}{2673777159018349407150951674140654501417209372773697144879199}\cdot t^{41}+\frac{270139225865718160195108344281932513837801800623180891113104471174502761}{13368885795091747035754758370703272507086046863868485724395995}\cdot t^{39}-\frac{17504377904101596324033875460615292446178822651324970164047245890301448738}{13368885795091747035754758370703272507086046863868485724395995}\cdot t^{37}+\frac{241417111308022751864593268607034332250795315103703849454133955564304569447}{3819681655740499153072788105915220716310299103962424492684570}\cdot t^{35}-\frac{417461700998832535888013611098024544562877467942324143962594819500204690781}{179749724976023489556366499101892739591072899009996446714568}\cdot t^{33}+\frac{11833124815712400135842891392595595983654814682158272437444748426823268990941}{179749724976023489556366499101892739591072899009996446714568}\cdot t^{31}-\frac{65165868115924387729781881637135629235178218465798489454766856472128902988721}{44937431244005872389091624775473184897768224752499111678642}\cdot t^{29}+\frac{8950788662231343960452674223015799328490570268347831181034833114831557404985109}{359499449952046979112732998203785479182145798019992893429136}\cdot t^{27}-\frac{478704604960351410779604889112841913775000825638222055051857637740032525024761199}{1437997799808187916450931992815141916728583192079971573716544}\cdot t^{25}+\frac{9925205754099903992553488640215308858331468615839994274306524619215335991007244275}{2875995599616375832901863985630283833457166384159943147433088}\cdot t^{23}-\frac{39574139335929622090218291359111702868526202003796846493389357737827545370563481575}{1437997799808187916450931992815141916728583192079971573716544}\cdot t^{21}+\frac{959679939494772111300095491567779447971265584280337997759441524927235123645790698775}{5751991199232751665803727971260567666914332768319886294866176}\cdot t^{19}-\frac{17407759974371305510851577309773201151358368218183300079338711488876167728387966689925}{23007964796931006663214911885042270667657331073279545179464704}\cdot t^{17}+\frac{231107909475706326627691901134502903421125973185867597809021172619011327743453198028925}{92031859187724026652859647540169082670629324293118180717858816}\cdot t^{15}-\frac{136357013049767876297511486299289011288401698361873891793964289604094336648170198164125}{23007964796931006663214911885042270667657331073279545179464704}\cdot t^{13}+\frac{1761418209594722333901829030194948916548460194532685593063371761972011537125645409598625}{184063718375448053305719295080338165341258648586236361435717632}\cdot t^{11}-\frac{7387857336351549913771532876087718967575365919608623360960897960220381728355933207166375}{736254873501792213222877180321352661365034594344945445742870528}\cdot t^9+\frac{9356886813252807854531678472081294769264238391312320572101476127424066279255908821256375}{1472509747003584426445754360642705322730069188689890891485741056}\cdot t^7-\frac{1609825480084081931092000503540531282857440951522146126162858258795233268719628996693375}{736254873501792213222877180321352661365034594344945445742870528}\cdot t^5+\frac{1013703806628898957584380458829141478411679999112634787026078637511327054721251963544375}{2945019494007168852891508721285410645460138377379781782971482112}\cdot t^3-\frac{198168884362339221527978734021707856831204359536056833247274128392041896735597582655625}{11780077976028675411566034885141642581840553509519127131885928448}\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.