Rule: Q[2, 10, 30]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{12}-\frac{8477}{152}\cdot t^{10}+\frac{155745}{152}\cdot t^8-\frac{563535}{76}\cdot t^6+\frac{1500975}{76}\cdot t^4-\frac{2132865}{152}\cdot t^2+\frac{110565}{152}$
• $P_3$:
  $t^{42}-\frac{61207353021989050186093439767945403405255979935645700964984353136634333843}{92336983841822717755850607896184354252299781868834296552741822537011318}\cdot t^{40}+\frac{13420370807049796208295901872713657202189000795399043272735951035099306363972295}{67960020107581520268306047411591684729692639455462042262817981387240330048}\cdot t^{38}-\frac{26214145493621980678309982576576547995642860370641859169536765486511102402132729195}{747560221183396722951366521527508532026619034010082464890997795259643630528}\cdot t^{36}+\frac{3103346060075376926042638835741119294174124878367670137759342179515564029333826669825}{747560221183396722951366521527508532026619034010082464890997795259643630528}\cdot t^{34}-\frac{259573749563028979417813224719398014512206423844294372800092489751766805223221234871635}{747560221183396722951366521527508532026619034010082464890997795259643630528}\cdot t^{32}+\frac{360547827632354176332942505413128826467963873513377896149726880061897178642573333573265}{16990005026895380067076511852897921182423159863865510565704495346810082512}\cdot t^{30}-\frac{180686737462785097052861051865904484853770725909149988675975040504750798841463069551281325}{186890055295849180737841630381877133006654758502520616222749448814910907632}\cdot t^{28}+\frac{6206318690884347465911891484413974937155144445296058534252129474007228973716502636666345575}{186890055295849180737841630381877133006654758502520616222749448814910907632}\cdot t^{26}-\frac{161540928928425090744642261875998184240530507735278809090048119892103951314807497494746923125}{186890055295849180737841630381877133006654758502520616222749448814910907632}\cdot t^{24}+\frac{277071933041578574054074511199400881144873362034800657498878009496125358188095955480626191625}{16251309156160798325029706989728446348404761608914836193282560766513991968}\cdot t^{22}-\frac{374836192373764589872406770581405023171003978829514433626934527847339422415820647703059434125}{1477391741469163484093609726338949668036796509901348744843869160592181088}\cdot t^{20}+\frac{219553837522534815884474972017378828302444272519820918317268696406359553540036764524831608125}{77757460077324393899663669807313140422989289994807828675993113715377952}\cdot t^{18}-\frac{1802867031738013394252727190248765040206620540744531613780078434189666042261916356253946314375}{77757460077324393899663669807313140422989289994807828675993113715377952}\cdot t^{16}+\frac{5359540618999275141430210033047357267884860837436242003176221995115018107112048275771988953125}{38878730038662196949831834903656570211494644997403914337996556857688976}\cdot t^{14}-\frac{22482154419892454931000840100689589383634455961578948317516369690535575255869287753051138061875}{38878730038662196949831834903656570211494644997403914337996556857688976}\cdot t^{12}+\frac{64175841125614442952694195080644895568136430466101324394949091960367727964827445116097673355625}{38878730038662196949831834903656570211494644997403914337996556857688976}\cdot t^{10}-\frac{118290644395928218235500388772577532697406733017158799511007080804410747368526242061643855071875}{38878730038662196949831834903656570211494644997403914337996556857688976}\cdot t^8+\frac{519796128616516583179568234614320354159727963711016563950626264104035607903107017302242350146875}{155514920154648787799327339614626280845978579989615657351986227430755904}\cdot t^6-\frac{298676285382693432669654619641981516874693532823339154834807060756894544596165858494904241578125}{155514920154648787799327339614626280845978579989615657351986227430755904}\cdot t^4+\frac{70117914651742730189419949334386424875740744562614615560752631290100557783984650229459074734375}{155514920154648787799327339614626280845978579989615657351986227430755904}\cdot t^2-\frac{3084528772947522571400972385646213792530185742408354826094849505259273182787353840683984953125}{155514920154648787799327339614626280845978579989615657351986227430755904}$

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.