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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{12}-\frac{8477}{76}\cdot t^{10}+\frac{155745}{152}\cdot t^8-\frac{563535}{152}\cdot t^6+\frac{1500975}{304}\cdot t^4-\frac{2132865}{1216}\cdot t^2+\frac{110565}{2432}$
• $P_3$:
  $4\cdot t^{42}-\frac{61207353021989050186093439767945403405255979935645700964984353136634333843}{46168491920911358877925303948092177126149890934417148276370911268505659}\cdot t^{40}+\frac{13420370807049796208295901872713657202189000795399043272735951035099306363972295}{67960020107581520268306047411591684729692639455462042262817981387240330048}\cdot t^{38}-\frac{26214145493621980678309982576576547995642860370641859169536765486511102402132729195}{1495120442366793445902733043055017064053238068020164929781995590519287261056}\cdot t^{36}+\frac{3103346060075376926042638835741119294174124878367670137759342179515564029333826669825}{2990240884733586891805466086110034128106476136040329859563991181038574522112}\cdot t^{34}-\frac{259573749563028979417813224719398014512206423844294372800092489751766805223221234871635}{5980481769467173783610932172220068256212952272080659719127982362077149044224}\cdot t^{32}+\frac{360547827632354176332942505413128826467963873513377896149726880061897178642573333573265}{271840080430326081073224189646366738918770557821848169051271925548961320192}\cdot t^{30}-\frac{180686737462785097052861051865904484853770725909149988675975040504750798841463069551281325}{5980481769467173783610932172220068256212952272080659719127982362077149044224}\cdot t^{28}+\frac{6206318690884347465911891484413974937155144445296058534252129474007228973716502636666345575}{11960963538934347567221864344440136512425904544161319438255964724154298088448}\cdot t^{26}-\frac{161540928928425090744642261875998184240530507735278809090048119892103951314807497494746923125}{23921927077868695134443728688880273024851809088322638876511929448308596176896}\cdot t^{24}+\frac{277071933041578574054074511199400881144873362034800657498878009496125358188095955480626191625}{4160335143977164371207604989370482265191618971882198065480335556227581943808}\cdot t^{22}-\frac{374836192373764589872406770581405023171003978829514433626934527847339422415820647703059434125}{756424571632211703855928179885542230034839813069490557360061010223196717056}\cdot t^{20}+\frac{219553837522534815884474972017378828302444272519820918317268696406359553540036764524831608125}{79623639119180179353255597882688655793141032954683216564216948444547022848}\cdot t^{18}-\frac{1802867031738013394252727190248765040206620540744531613780078434189666042261916356253946314375}{159247278238360358706511195765377311586282065909366433128433896889094045696}\cdot t^{16}+\frac{5359540618999275141430210033047357267884860837436242003176221995115018107112048275771988953125}{159247278238360358706511195765377311586282065909366433128433896889094045696}\cdot t^{14}-\frac{22482154419892454931000840100689589383634455961578948317516369690535575255869287753051138061875}{318494556476720717413022391530754623172564131818732866256867793778188091392}\cdot t^{12}+\frac{64175841125614442952694195080644895568136430466101324394949091960367727964827445116097673355625}{636989112953441434826044783061509246345128263637465732513735587556376182784}\cdot t^{10}-\frac{118290644395928218235500388772577532697406733017158799511007080804410747368526242061643855071875}{1273978225906882869652089566123018492690256527274931465027471175112752365568}\cdot t^8+\frac{519796128616516583179568234614320354159727963711016563950626264104035607903107017302242350146875}{10191825807255062957216716528984147941522052218199451720219769400902018924544}\cdot t^6-\frac{298676285382693432669654619641981516874693532823339154834807060756894544596165858494904241578125}{20383651614510125914433433057968295883044104436398903440439538801804037849088}\cdot t^4+\frac{70117914651742730189419949334386424875740744562614615560752631290100557783984650229459074734375}{40767303229020251828866866115936591766088208872797806880879077603608075698176}\cdot t^2-\frac{3084528772947522571400972385646213792530185742408354826094849505259273182787353840683984953125}{81534606458040503657733732231873183532176417745595613761758155207216151396352}$

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 (physicists') type can be downloaded here packed into a single file.