Rule: Q[4, 65]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{69}-\frac{521877709613238659888948781480433475007384979512642602321225392}{29435603524201073832079503952842058087131298266682789732649}\cdot t^{67}+\frac{16596066868956950347222467369435182591244024839689965756340300496508}{1795571814976265503756849741123365543315009194267650173691589}\cdot t^{65}-\frac{5416964013885172881397268665871933704821614800563546904076013066306240}{1795571814976265503756849741123365543315009194267650173691589}\cdot t^{63}+\frac{40092547222520939440063210056110236593391682084040341999425785693909240}{57921671450847274314737088423334372365000296589279037861019}\cdot t^{61}-\frac{112827388175334250335289481566992973433581753203482510712871706237128920}{949535597554873349421919482349743809262299944086541604279}\cdot t^{59}+\frac{15060366629596868807098204601413200460364604029605700443888535240483754810}{949535597554873349421919482349743809262299944086541604279}\cdot t^{57}-\frac{1603839970519617246188219682862384219538086045092231357751758905836151279340}{949535597554873349421919482349743809262299944086541604279}\cdot t^{55}+\frac{554954637104762342559718347564067550237722868606840805716059914806804064715725}{3798142390219493397687677929398975237049199776346166417116}\cdot t^{53}-\frac{39501098106811423897747507124072202827881543388984832516407402031019133021435475}{3798142390219493397687677929398975237049199776346166417116}\cdot t^{51}+\frac{9341121604013653962614807283521516146041582034928548109798668982705563921046907375}{15192569560877973590750711717595900948196799105384665668464}\cdot t^{49}-\frac{115443967049865695100038131329530930845350769617565666667264547508841873428173191625}{3798142390219493397687677929398975237049199776346166417116}\cdot t^{47}+\frac{38356335108543392715406191215901705719863725490883875837715407302637640679161137142625}{30385139121755947181501423435191801896393598210769331336928}\cdot t^{45}-\frac{1342400942198001516644750598990537157430008263985932086995701013515003833579459102908125}{30385139121755947181501423435191801896393598210769331336928}\cdot t^{43}+\frac{3688994375165634386142780161448161682923926145613668286676523238249884735783244849418125}{2826524569465669505255946366064353664780799833559937798784}\cdot t^{41}-\frac{46013593570505142912178020691748183065577210025851388447607319737209873220191513653795625}{1413262284732834752627973183032176832390399916779968899392}\cdot t^{39}+\frac{30996363420243278485552103860731120245747418725735383036528011766147131478632520087667364375}{45224393111450712084095141857029658636492797336959004780544}\cdot t^{37}-\frac{549632519078597704101199093591044322789985953882387513694046828274981344268667789307276448125}{45224393111450712084095141857029658636492797336959004780544}\cdot t^{35}+\frac{32743992051898957009846031162314819594097721958615090216456374546284269111528113216636131053125}{180897572445802848336380567428118634545971189347836019122176}\cdot t^{33}-\frac{50996840343824804037498851368638235308275386578261539387772061676246705660116488072490391465625}{22612196555725356042047570928514829318246398668479502390272}\cdot t^{31}+\frac{4230421357854403694039041699361772591514963067966436803295762616894571623148921894642240078709375}{180897572445802848336380567428118634545971189347836019122176}\cdot t^{29}-\frac{36270899507518334722792660113557966258994007019257078801051195215663917786600594760378592286784375}{180897572445802848336380567428118634545971189347836019122176}\cdot t^{27}+\frac{1020345468497309486427817335663225615907351843802835840821038834054748418327422546536506041217065625}{723590289783211393345522269712474538183884757391344076488704}\cdot t^{25}-\frac{2914613521599129937616137192661383771906776030778458155089889976532373683653797354213585652936796875}{361795144891605696672761134856237269091942378695672038244352}\cdot t^{23}+\frac{213889352632772935106439000317640115091521476243591211039609363984973975421707348745741833505463359375}{5788722318265691146764178157699796305471078059130752611909632}\cdot t^{21}-\frac{776436531236095967454353045771304640498021769956335019648860750480606237231160566858655464963908765625}{5788722318265691146764178157699796305471078059130752611909632}\cdot t^{19}+\frac{8769141233881929785482412546834239474838229789273388538695284879318014461711895853876476738447718703125}{23154889273062764587056712630799185221884312236523010447638528}\cdot t^{17}-\frac{4712530801106280311948669335777060465051056428910431415567708942121418372466750288666752449123058390625}{5788722318265691146764178157699796305471078059130752611909632}\cdot t^{15}+\frac{60062191957458320431492034020484037940545527975106563314404352252697961099294225243764858460932725078125}{46309778546125529174113425261598370443768624473046020895277056}\cdot t^{13}-\frac{68508687042331460252896847730752972279700139519495133972991147724989914885131927692695637599301301640625}{46309778546125529174113425261598370443768624473046020895277056}\cdot t^{11}+\frac{213654116728520262920479570916011744078097553290038188341291196162579308472449712882240279924342634921875}{185239114184502116696453701046393481775074497892184083581108224}\cdot t^9-\frac{53284509398383316880977644022923658540170609754829275662304586013432512606792022991980352027126433046875}{92619557092251058348226850523196740887537248946092041790554112}\cdot t^7+\frac{980622025493784862835320565961388904080776929765808078137148826886104523631685793230498891877143605703125}{5927651653904067734286518433484591416802383932549890674595463168}\cdot t^5-\frac{134476195393791319976080707530623082020134365536929586973499611392480512600073087008026306653456449609375}{5927651653904067734286518433484591416802383932549890674595463168}\cdot t^3+\frac{22452868708068534800025851222020511794115306234898298838830003507884581372433749355588545151782405859375}{23710606615616270937146073733938365667209535730199562698381852672}\cdot t$

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.