Rule: Q[4, 69]

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^{73}-\frac{11239475515162231385079472708356306542995635977836634110572561959256}{564032284581165233520782981146660289488340845610857060255025647}\cdot t^{71}+\frac{429601268002075908380884488219995080522556227198318731275520200367218832}{36662098497775740178850893774532918816742154964705708916576667055}\cdot t^{69}-\frac{158769900454267181661905402899376704714259338504396501340387636878549407186}{36662098497775740178850893774532918816742154964705708916576667055}\cdot t^{67}+\frac{3764937673682516660333826348404315493355468771391642827444500330861108888609}{3332918045252340016259172161321174437885650451336882628779697005}\cdot t^{65}-\frac{11353218979203374808577986890830820908472434338796561984035468387984566407668}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{63}+\frac{1738390569668615218946830200179879900599636527758997294795136390815574868950728}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{61}-\frac{213422715117177444811077559422359985070249437564687049056438080922576984894100419}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{59}+\frac{85591167853555232588642672399231751049170389436537946391851678837320102752991434553}{205102648938605539462102902235149196177578489313038931001827508}\cdot t^{57}-\frac{14203956381835021570201122469743339560638517503385067668265876255822082892624630581659}{410205297877211078924205804470298392355156978626077862003655016}\cdot t^{55}+\frac{492515308672834760699260541700165247340922123284763578278169345351875574609631051798345}{205102648938605539462102902235149196177578489313038931001827508}\cdot t^{53}-\frac{230035672127815370190304642588884773233329314239771625468823599585221139037448901271665985}{1640821191508844315696823217881193569420627914504311448014620064}\cdot t^{51}+\frac{22733078476645044829343637555633133208353894975158388782841799037688918963622716981335740025}{3281642383017688631393646435762387138841255829008622896029240128}\cdot t^{49}-\frac{954248361223518566170339284147740887111460535424507848248727143988717753454121866868313079575}{3281642383017688631393646435762387138841255829008622896029240128}\cdot t^{47}+\frac{17055468993213985308956435928151427686035078455713101588044898401694598659036726748178373871275}{1640821191508844315696823217881193569420627914504311448014620064}\cdot t^{45}-\frac{4159004079870645284244631589934427226927778398421138535106159747165822728061806997916301414628625}{13126569532070754525574585743049548555365023316034491584116960512}\cdot t^{43}+\frac{865089072644825363829692792334910609216032099606348395743850323827651661447792948881595927844140875}{105012556256566036204596685944396388442920186528275932672935684096}\cdot t^{41}-\frac{38349641625747759336801269821025883286101948654080776769156905463556406515807560964470826393732688875}{210025112513132072409193371888792776885840373056551865345871368192}\cdot t^{39}+\frac{361786375440376467495943800782574526772123873269380417992541334496624669372781275165600215902772913625}{105012556256566036204596685944396388442920186528275932672935684096}\cdot t^{37}-\frac{46376428456899291998065420979545594372502183221670228704858871478367254500292441272973639251904699581625}{840100450052528289636773487555171107543361492226207461383485472768}\cdot t^{35}+\frac{1258099055832246983875104736906273138100779491988347890513214270021631347548188880887778183328533287899375}{1680200900105056579273546975110342215086722984452414922766970945536}\cdot t^{33}-\frac{7192787527333224136268742436480245905356070744964817019135825054612308929813802320098064938169655443691875}{840100450052528289636773487555171107543361492226207461383485472768}\cdot t^{31}+\frac{34487153429729479497163623230287769739939410715290564661326723945083501449081900589457368241180071852644375}{420050225026264144818386743777585553771680746113103730691742736384}\cdot t^{29}-\frac{2204847764686595310652900054857279932629606754614057593371358602961118771241573110510605006173519663823118125}{3360401800210113158547093950220684430173445968904829845533941891072}\cdot t^{27}+\frac{58292718711206464769019371511033198269068790813530717315773492819650450177591783997709279651106448465897718125}{13441607200840452634188375800882737720693783875619319382135767564288}\cdot t^{25}-\frac{631550792459235557432028276120373092898771106833841822352505327809891958972078229923990773083047646494042171875}{26883214401680905268376751601765475441387567751238638764271535128576}\cdot t^{23}+\frac{1386673706753413753332601052157344591661497038338849291515801242548922373892950238402366673759449017000634140625}{13441607200840452634188375800882737720693783875619319382135767564288}\cdot t^{21}-\frac{38970208259149440594582655993016063044093529209102566448994332328038540758022746948885617489133279918965692715625}{107532857606723621073507006407061901765550271004954555057086140514304}\cdot t^{19}+\frac{215495937583443461933997977559589119719467268269835939687752800464323864882422213549332343903232728067804281403125}{215065715213447242147014012814123803531100542009909110114172281028608}\cdot t^{17}-\frac{459506318620166167821646345798573507496184152729594925108967936977117756631827410681404723871377195098827878565625}{215065715213447242147014012814123803531100542009909110114172281028608}\cdot t^{15}+\frac{368092864568411018836574541413515941271365428163184259415849132041458072070069385935083533555012158874116090203125}{107532857606723621073507006407061901765550271004954555057086140514304}\cdot t^{13}-\frac{3424076448939295295562620076176607065406300043094659461272696726150747828904022862133113982611549102933776294359375}{860262860853788968588056051256495214124402168039636440456689124114432}\cdot t^{11}+\frac{44066272116326541910790033708396174983536592998575203791879709761921263794385431639145722923990131508674758214953125}{13764205773660623497408896820103923425990434688634183047307025985830912}\cdot t^9-\frac{45703598946711829066686598069231368092718638906050157399519466712654447243897603747190888643433406797659030072140625}{27528411547321246994817793640207846851980869377268366094614051971661824}\cdot t^7+\frac{6833500832689231322046140068437014226158544187361564200879561502653340734370382550067085059566730703131768375296875}{13764205773660623497408896820103923425990434688634183047307025985830912}\cdot t^5-\frac{7716469243966586089876510817176331439722498843870811620499746716610251911396765669184502745822497803715590296796875}{110113646189284987979271174560831387407923477509073464378456207886647296}\cdot t^3+\frac{648800250868216572192932614330187149618583666558413767471608743496526824136819987508757309150915358403041926015625}{220227292378569975958542349121662774815846955018146928756912415773294592}\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.