Rule: Q[6, 53]

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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{59}-\frac{6577774559923300700287386592280220893010997637769794848959520}{132673921194919697215055115424737796685927620643991976099}\cdot t^{57}+\frac{7109305459977023591181186524076330375790196350911013302885427540}{398021763584759091645165346274213390057782861931975928297}\cdot t^{55}-\frac{74449254393772964029076111863638996304243817030020716166084429875130}{18707022888483677307322771274888029332715794510802868629959}\cdot t^{53}+\frac{1644114637476432882710895234222688513856393241500402827199264310592625}{2672431841211953901046110182126861333245113501543266947137}\cdot t^{51}-\frac{875092312374712103952413057945755686293467687545391599585538758348777575}{12471348592322451538215180849925352888477196340535245753306}\cdot t^{49}+\frac{1560367811123195124625010778297693348284440535087202397551962157640223375}{254517318210662276290105731631129650785248904908882566394}\cdot t^{47}-\frac{4554949172537596561807301314739707458393132769254609046411404230356165375}{10830524179177118140004499218345942586606336379101385804}\cdot t^{45}+\frac{498984515675288344700031285962222259665151075602238211907810178042285088875}{21661048358354236280008998436691885173212672758202771608}\cdot t^{43}-\frac{44154444737267688213234914497420528703201556286310790765968105023959202805625}{43322096716708472560017996873383770346425345516405543216}\cdot t^{41}+\frac{6362133319743129571162365018346516557507101947860640463779271045987989225912125}{173288386866833890240071987493535081385701382065622172864}\cdot t^{39}-\frac{375078813454556641849392388769930844920660069000498392807025188729362531553666875}{346576773733667780480143974987070162771402764131244345728}\cdot t^{37}+\frac{18146732720442866735398858105163732264141105938663898490031430120159591498969150625}{693153547467335560960287949974140325542805528262488691456}\cdot t^{35}-\frac{721168827062875188321806728870531964851515348222639465197145478752225096361864891875}{1386307094934671121920575899948280651085611056524977382912}\cdot t^{33}+\frac{5880845378509273933865961874192785795526761859832353342746303772445507234177959996875}{693153547467335560960287949974140325542805528262488691456}\cdot t^{31}-\frac{157064642256357322715804846414817759799902558849963517998328454389972274231720359393125}{1386307094934671121920575899948280651085611056524977382912}\cdot t^{29}+\frac{13362445744740286863122241719823995314556121027233577851069336825097422805993236296875}{10830524179177118140004499218345942586606336379101385804}\cdot t^{27}-\frac{3775061449632427528463460290329184888186973753986688610068504581949402705479100622265625}{346576773733667780480143974987070162771402764131244345728}\cdot t^{25}+\frac{3431457909645396039132575065909516061104067393029140770887811584292516814069642961254890625}{44361827037909475901458428798344980834739553808799276253184}\cdot t^{23}-\frac{38801406986785180507445473313236612391569366694628403355281078690703161884580833043935234375}{88723654075818951802916857596689961669479107617598552506368}\cdot t^{21}+\frac{344691856757157634765926268168141132265690213380672046243318160605729639228519168786658703125}{177447308151637903605833715193379923338958215235197105012736}\cdot t^{19}-\frac{2364409103389564646557219884219531593832486673925076721793357281947524556678276967387790859375}{354894616303275807211667430386759846677916430470394210025472}\cdot t^{17}+\frac{6121061682853995741517331061532676533796367153829051093952690281616109925650488299163024765625}{354894616303275807211667430386759846677916430470394210025472}\cdot t^{15}-\frac{23205073605896841086743901186261945939767328316540385423998149339240769502406093569303545234375}{709789232606551614423334860773519693355832860940788420050944}\cdot t^{13}+\frac{61764730945655834205926395233275653792885466455244631642122791484667382522438471616466249609375}{1419578465213103228846669721547039386711665721881576840101888}\cdot t^{11}-\frac{108681405463364877931730936138327601583208730292026741248918364626163405542344729995832848703125}{2839156930426206457693339443094078773423331443763153680203776}\cdot t^9+\frac{230668175568733918641390634649229670502990146788436910545245406229052798030182942144993969296875}{11356627721704825830773357772376315093693325775052614720815104}\cdot t^7-\frac{126457235627289748868856653701483607915443175041492575578772627945047164916971063680196281328125}{22713255443409651661546715544752630187386651550105229441630208}\cdot t^5+\frac{26085629682060700133836439328208572475254833041841586110129529979524912615708701351635455234375}{45426510886819303323093431089505260374773303100210458883260416}\cdot t^3-\frac{626857223464107267939842839050165807456308493211356266943681713189458130045065848652658203125}{90853021773638606646186862179010520749546606200420917766520832}\cdot t$

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.