Rule: Q[4, 53]

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^{57}-\frac{3738560480187344376501980021633463109684731183}{2452070369646233148101113457952700592074375}\cdot t^{55}+\frac{129779700457856755078652986017815704963670965022352}{120151448112665424256954559439682329011644375}\cdot t^{53}-\frac{56804670188253191865034240762097096918352198954683001}{120151448112665424256954559439682329011644375}\cdot t^{51}+\frac{689204639176661967004010848285006854123489954569297433}{4806057924506616970278182377587293160465775}\cdot t^{49}-\frac{3143472473091549111804499431927092550543538849654425594}{98082814785849325924044538318108023682975}\cdot t^{47}+\frac{537314010255767831877366743657006751271935426217757479008}{98082814785849325924044538318108023682975}\cdot t^{45}-\frac{71975733958726497867024071559312521588012495242188283612878}{98082814785849325924044538318108023682975}\cdot t^{43}+\frac{7681196484177677448722115021066351333179038919597442061684119}{98082814785849325924044538318108023682975}\cdot t^{41}-\frac{132081100422742762228970186490994270666206014855685257194833633}{19616562957169865184808907663621604736595}\cdot t^{39}+\frac{9216556685759130054901788158463876875789074463644007630563100736}{19616562957169865184808907663621604736595}\cdot t^{37}-\frac{524305775818059519489424649759267118515056145279269577097941063343}{19616562957169865184808907663621604736595}\cdot t^{35}+\frac{24366565754024542399946839304530554594169843944638856386298259261893}{19616562957169865184808907663621604736595}\cdot t^{33}-\frac{925126476391350951403085218500113919020636100685150734282854713115244}{19616562957169865184808907663621604736595}\cdot t^{31}+\frac{5727991429284773325273093778163660165081576292140941271477944509037056}{3923312591433973036961781532724320947319}\cdot t^{29}-\frac{144040090378495622980236680333468179182181930902883590381021374500389012}{3923312591433973036961781532724320947319}\cdot t^{27}+\frac{2925258296499224360798384470215148186776443200636796944688276230106444685}{3923312591433973036961781532724320947319}\cdot t^{25}-\frac{47598962689173461933335731958732894101587545362888563745629576150575766985}{3923312591433973036961781532724320947319}\cdot t^{23}+\frac{614127301309839199388645479294230609108496384703486728400972040755245158480}{3923312591433973036961781532724320947319}\cdot t^{21}-\frac{6199101455615213327568631954207019595541967780606181462066659171582072237775}{3923312591433973036961781532724320947319}\cdot t^{19}+\frac{48125184607085459638407602219682641533826405637366801795466718718970412967675}{3923312591433973036961781532724320947319}\cdot t^{17}-\frac{281090184683657654815369414117342970332141363351822054937446669094258974921050}{3923312591433973036961781532724320947319}\cdot t^{15}+\frac{1200436701811121540498812868207729947913621028729091393772688681889550119840800}{3923312591433973036961781532724320947319}\cdot t^{13}-\frac{3608739317798414804141109411862142880934308919662114175020338805485477681691150}{3923312591433973036961781532724320947319}\cdot t^{11}+\frac{7247947264735037025073328547528886088855061820657379766651998153267808462274125}{3923312591433973036961781532724320947319}\cdot t^9-\frac{9019065417719865757945641029483907669254906708187912205195715531218103545108875}{3923312591433973036961781532724320947319}\cdot t^7+\frac{6182806930116120375496226971835082262725981629937903416368087893170328576367200}{3923312591433973036961781532724320947319}\cdot t^5-\frac{1897945078608167609349683393488942288554765156353235921551811985119140078546325}{3923312591433973036961781532724320947319}\cdot t^3+\frac{163077940747771505123925641765563019736507960416332684540919985583616370623475}{3923312591433973036961781532724320947319}\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.