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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^9-21\cdot t^7+108\cdot t^5-135\cdot t^3+45\cdot t$
• $P_3$:
  $t^{47}-\frac{151302055808386406235788351169912012422458547913802523758603416}{157281009354020553361820686714156147142188786633746890875247}\cdot t^{45}+\frac{161237173071669896791070725028756359330738100067290442957715631274}{381968165574049915307278810591522071631029910396242449268457}\cdot t^{43}-\frac{299902668353958550999275199492552046942288160033885586653045150110877}{2673777159018349407150951674140654501417209372773697144879199}\cdot t^{41}+\frac{270139225865718160195108344281932513837801800623180891113104471174502761}{13368885795091747035754758370703272507086046863868485724395995}\cdot t^{39}-\frac{35008755808203192648067750921230584892357645302649940328094491780602897476}{13368885795091747035754758370703272507086046863868485724395995}\cdot t^{37}+\frac{482834222616045503729186537214068664501590630207407698908267911128609138894}{1909840827870249576536394052957610358155149551981212246342285}\cdot t^{35}-\frac{417461700998832535888013611098024544562877467942324143962594819500204690781}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{33}+\frac{23666249631424800271685782785191191967309629364316544874889496853646537981882}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{31}-\frac{1042653889854790203676510106194170067762851495452775831276269703554062447819536}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{29}+\frac{35803154648925375841810696892063197313962281073391324724139332459326229619940436}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{27}-\frac{957409209920702821559209778225683827550001651276444110103715275480065050049522398}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{25}+\frac{19850411508199807985106977280430617716662937231679988548613049238430671982014488550}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{23}-\frac{316593114687436976721746330872893622948209616030374771947114861902620362964507852600}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{21}+\frac{3838719757979088445200381966271117791885062337121351991037766099708940494583162795100}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{19}-\frac{34815519948742611021703154619546402302716736436366600158677422977752335456775933379850}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{17}+\frac{231107909475706326627691901134502903421125973185867597809021172619011327743453198028925}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{15}-\frac{1090856104398143010380091890394312090307213586894991134351714316832754693185361585313000}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{13}+\frac{3522836419189444667803658060389897833096920389065371186126743523944023074251290819197250}{22468715622002936194545812387736592448884112376249555839321}\cdot t^{11}-\frac{7387857336351549913771532876087718967575365919608623360960897960220381728355933207166375}{22468715622002936194545812387736592448884112376249555839321}\cdot t^9+\frac{9356886813252807854531678472081294769264238391312320572101476127424066279255908821256375}{22468715622002936194545812387736592448884112376249555839321}\cdot t^7-\frac{6439301920336327724368002014162125131429763806088584504651433035180933074878515986773500}{22468715622002936194545812387736592448884112376249555839321}\cdot t^5+\frac{2027407613257797915168760917658282956823359998225269574052157275022654109442503927088750}{22468715622002936194545812387736592448884112376249555839321}\cdot t^3-\frac{198168884362339221527978734021707856831204359536056833247274128392041896735597582655625}{22468715622002936194545812387736592448884112376249555839321}\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.