Rule: Q[4, 7, 42]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{11}-41\cdot t^9+528\cdot t^7-2520\cdot t^5+4095\cdot t^3-1575\cdot t$
• $P_3$:
  $t^{53}-\frac{15767333081375341737723581901043029147232858209489011672160283897003807298951}{12172946534731404259994921631531913551723325534407284336727305941037734402}\cdot t^{51}+\frac{345792102701007820316307325774342704052706444046638954170893106972790542378858785}{450399021785061957619812100366680801413763044773069520458910319818396172874}\cdot t^{49}-\frac{62374116066591860369371366533819933204872997053474302072525524589587910306385613657}{225199510892530978809906050183340400706881522386534760229455159909198086437}\cdot t^{47}+\frac{15363094522379800363025724339352992881157304878289759464920368630977069822354959033235}{225199510892530978809906050183340400706881522386534760229455159909198086437}\cdot t^{45}-\frac{2746539313221555841428329734499334148323949964868491524148216810669467630417413288825060}{225199510892530978809906050183340400706881522386534760229455159909198086437}\cdot t^{43}+\frac{369838502195314343538092352487399461076816484582542098546852365127256043327031019037131470}{225199510892530978809906050183340400706881522386534760229455159909198086437}\cdot t^{41}-\frac{38419260470448634277199514212340951805874203529857887322265027440125980776863115530599421875}{225199510892530978809906050183340400706881522386534760229455159909198086437}\cdot t^{39}+\frac{4449762295430423971000791673712187865718096049942738396994014167385340032808240088962146930}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{37}-\frac{573929144964966403140732628991280119305534435707039647716409588853992675636997577320947449125}{640681396564810750526048506922732292195964501810909701933016102159880758}\cdot t^{35}+\frac{29507184643949478593601088125910514219904822933918704413658527166418048622568738486289559177275}{640681396564810750526048506922732292195964501810909701933016102159880758}\cdot t^{33}-\frac{606788295300064404767433429942068727738198279104274539863224201972653612166885983749240669068150}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{31}+\frac{19981019133143070139544415855555694914213816725302519397655957663683774629032121909479979180274250}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{29}-\frac{526019505941375089854350338659962138086041404059324268241475278762282884412605234739950466084660300}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{27}+\frac{11030028478135654339952922146587589609759312370109926185978777434145412777504057536320329414518886000}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{25}-\frac{183110211388146793955055342168573900921673063562361421509070774123991365836802173846846299604247586250}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{23}+\frac{2385863160057886703553802456629312463917108649839639423064829682212715313829651923772578683209402169375}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{21}-\frac{48227230054961722719503346358058833304230386585118466834553445495294945566136990076466750361234951284375}{640681396564810750526048506922732292195964501810909701933016102159880758}\cdot t^{19}+\frac{372209852058176776776775450786136361523226364255206909916742824722562035559939855340148901447464700493125}{640681396564810750526048506922732292195964501810909701933016102159880758}\cdot t^{17}-\frac{1074263969982152291758628224950542755917583329342234627127495841087224264317580559259049815560619510721875}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{15}+\frac{4511186473705371948525056930663075034737519006485668680390828153771449799361194357539995267765551303465625}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{13}-\frac{13275076637172849463472883334828507315562345083127328317657923416531368516568531926978432513028375739275000}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^{11}+\frac{25996033695633918479486874574982081981962139287958172377649767370443395728677214733392152480333497490718750}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^9-\frac{31469298621941054344308140001781725247221874412162703326519750530756819627235062541118762304502152432565625}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^7+\frac{21068288220735252466816544507863729538874960959399226981218194631352567089607163353929164373208426984562500}{320340698282405375263024253461366146097982250905454850966508051079940379}\cdot t^5-\frac{12918673252209893224754169300657155335519160085431261363622093361927833713060258528914584046427006499234375}{640681396564810750526048506922732292195964501810909701933016102159880758}\cdot t^3+\frac{1188482173252745613881830180639479086036271425257587123484695822918877507087761617344111972337554040390625}{640681396564810750526048506922732292195964501810909701933016102159880758}\cdot t$

Warning: This rule has negative weights!

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.