Rule: Q[2, 67]

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^{69}-\frac{2495032925738033801974536347613906346637232782}{546783215030858425189388984905997240740705}\cdot t^{67}+\frac{1340174990871219949778894031766514904354720200886}{546783215030858425189388984905997240740705}\cdot t^{65}-\frac{6939842837550622482753936519410363069897119901448}{8412049462013206541375215152399957549857}\cdot t^{63}+\frac{1643470427319763052592489476242107363407423090328414}{8412049462013206541375215152399957549857}\cdot t^{61}-\frac{291473565111813911659629378542018251154846756602997805}{8412049462013206541375215152399957549857}\cdot t^{59}+\frac{40235881991937853084404964666349291047774761251121482994}{8412049462013206541375215152399957549857}\cdot t^{57}-\frac{466949897900194871176093285306989757420651469479186347501}{885478890738232267513180542357890268406}\cdot t^{55}+\frac{334918889833623112714450293503707606533994309429099312562445}{7083831125905858140105444338863122147248}\cdot t^{53}-\frac{49474407566268045919348613626121332050709717335214000686804195}{14167662251811716280210888677726244294496}\cdot t^{51}+\frac{178758794167538407178234392009197872962054480683563816521427625}{833391897165395075306522863395661429088}\cdot t^{49}-\frac{9193570296127647780858177450656287402869194778156743337708694275}{833391897165395075306522863395661429088}\cdot t^{47}+\frac{1591172635808842679492157666780081839695612496457444977113729830675}{3333567588661580301226091453582645716352}\cdot t^{45}-\frac{116208511771746200689361796864481026152657601259985656096521062336625}{6667135177323160602452182907165291432704}\cdot t^{43}+\frac{14014024276088450910019231599983857419507731573273106409295162740500}{26043496786418596103328839481114419659}\cdot t^{41}-\frac{187367590551276463522153431790401464159939717226844021293732108765298125}{13334270354646321204904365814330582865408}\cdot t^{39}+\frac{66176332390394615378644136649212784609789674072112604491906250701687638625}{213348325674341139278469853029289325846528}\cdot t^{37}-\frac{2465491745453323910639533191892617447904837695245796846878049817675548612375}{426696651348682278556939706058578651693056}\cdot t^{35}+\frac{38649024140815471366245824251640687604237765408932039918848460532710110899375}{426696651348682278556939706058578651693056}\cdot t^{33}-\frac{253919011325155233805806106427407778702090306815621671103704292723156880075625}{213348325674341139278469853029289325846528}\cdot t^{31}+\frac{11128799096590733415202237936876789707988535161219927990439664973265449810171875}{853393302697364557113879412117157303386112}\cdot t^{29}-\frac{202040373886860470196400177214329608989044173739926666641436886474812690805325625}{1706786605394729114227758824234314606772224}\cdot t^{27}+\frac{753548997717174240026256110963789665362486481379432825445058270417490528789911875}{853393302697364557113879412117157303386112}\cdot t^{25}-\frac{18293019475474696009590300393497219866198552096857485361814004478503679425204109375}{3413573210789458228455517648468629213544448}\cdot t^{23}+\frac{713807411609474366113233611124763576817342763984271824190083613561237383189976828125}{27308585686315665827644141187749033708355584}\cdot t^{21}-\frac{5512577016826032024105440267519312813923831282228845331238884321542784785184315171875}{54617171372631331655288282375498067416711168}\cdot t^{19}+\frac{16538237956127961014596381009076818858106137544908789519558891066312904217672174478125}{54617171372631331655288282375498067416711168}\cdot t^{17}-\frac{37648271562737777720033865431251206242322147128089705107318184280673331300038747215625}{54617171372631331655288282375498067416711168}\cdot t^{15}+\frac{252335134269760735524798562408428181870605164406401774573660377401967334277884579203125}{218468685490525326621153129501992269666844672}\cdot t^{13}-\frac{597932485582106026746509119256304852415722399222972391231375209328034666787149214984375}{436937370981050653242306259003984539333689344}\cdot t^{11}+\frac{118518233188167337632180784151645916520295732502560102745270675100860736063057636640625}{109234342745262663310576564750996134833422336}\cdot t^9-\frac{464563843031699817917202093555353671875042960850942602580728145845895096199505653484375}{873874741962101306484612518007969078667378688}\cdot t^7+\frac{3975209459133147321427136040878923051998897418390088997716282651392783054791452703796875}{27963991742787241807507600576255010517356118016}\cdot t^5-\frac{931060171646498955976863666492918954336316287225842626768157506485959878632756377578125}{55927983485574483615015201152510021034712236032}\cdot t^3+\frac{29007856600718526577809681256341471211507888733963533943229370206076900323325392890625}{55927983485574483615015201152510021034712236032}\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.