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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{59}-\frac{205555454997603146883980831008756902906593676180306089029985}{132673921194919697215055115424737796685927620643991976099}\cdot t^{57}+\frac{1777326364994255897795296631019082593947549087727753325721356885}{1592087054339036366580661385096853560231131447727903713188}\cdot t^{55}-\frac{37224627196886482014538055931819498152121908515010358083042214937565}{74828091553934709229291085099552117330863178043211474519836}\cdot t^{53}+\frac{1644114637476432882710895234222688513856393241500402827199264310592625}{10689727364847815604184440728507445332980454006173067788548}\cdot t^{51}-\frac{875092312374712103952413057945755686293467687545391599585538758348777575}{24942697184644903076430361699850705776954392681070491506612}\cdot t^{49}+\frac{1560367811123195124625010778297693348284440535087202397551962157640223375}{254517318210662276290105731631129650785248904908882566394}\cdot t^{47}-\frac{4554949172537596561807301314739707458393132769254609046411404230356165375}{5415262089588559070002249609172971293303168189550692902}\cdot t^{45}+\frac{498984515675288344700031285962222259665151075602238211907810178042285088875}{5415262089588559070002249609172971293303168189550692902}\cdot t^{43}-\frac{44154444737267688213234914497420528703201556286310790765968105023959202805625}{5415262089588559070002249609172971293303168189550692902}\cdot t^{41}+\frac{6362133319743129571162365018346516557507101947860640463779271045987989225912125}{10830524179177118140004499218345942586606336379101385804}\cdot t^{39}-\frac{375078813454556641849392388769930844920660069000498392807025188729362531553666875}{10830524179177118140004499218345942586606336379101385804}\cdot t^{37}+\frac{18146732720442866735398858105163732264141105938663898490031430120159591498969150625}{10830524179177118140004499218345942586606336379101385804}\cdot t^{35}-\frac{721168827062875188321806728870531964851515348222639465197145478752225096361864891875}{10830524179177118140004499218345942586606336379101385804}\cdot t^{33}+\frac{5880845378509273933865961874192785795526761859832353342746303772445507234177959996875}{2707631044794279535001124804586485646651584094775346451}\cdot t^{31}-\frac{157064642256357322715804846414817759799902558849963517998328454389972274231720359393125}{2707631044794279535001124804586485646651584094775346451}\cdot t^{29}+\frac{3420786110653513436959293880274942800526366982971795929873750227224940238334268492000000}{2707631044794279535001124804586485646651584094775346451}\cdot t^{27}-\frac{60400983194118840455415364645266958210991580063787017761096073311190443287665609956250000}{2707631044794279535001124804586485646651584094775346451}\cdot t^{25}+\frac{3431457909645396039132575065909516061104067393029140770887811584292516814069642961254890625}{10830524179177118140004499218345942586606336379101385804}\cdot t^{23}-\frac{38801406986785180507445473313236612391569366694628403355281078690703161884580833043935234375}{10830524179177118140004499218345942586606336379101385804}\cdot t^{21}+\frac{344691856757157634765926268168141132265690213380672046243318160605729639228519168786658703125}{10830524179177118140004499218345942586606336379101385804}\cdot t^{19}-\frac{2364409103389564646557219884219531593832486673925076721793357281947524556678276967387790859375}{10830524179177118140004499218345942586606336379101385804}\cdot t^{17}+\frac{6121061682853995741517331061532676533796367153829051093952690281616109925650488299163024765625}{5415262089588559070002249609172971293303168189550692902}\cdot t^{15}-\frac{23205073605896841086743901186261945939767328316540385423998149339240769502406093569303545234375}{5415262089588559070002249609172971293303168189550692902}\cdot t^{13}+\frac{61764730945655834205926395233275653792885466455244631642122791484667382522438471616466249609375}{5415262089588559070002249609172971293303168189550692902}\cdot t^{11}-\frac{108681405463364877931730936138327601583208730292026741248918364626163405542344729995832848703125}{5415262089588559070002249609172971293303168189550692902}\cdot t^9+\frac{230668175568733918641390634649229670502990146788436910545245406229052798030182942144993969296875}{10830524179177118140004499218345942586606336379101385804}\cdot t^7-\frac{126457235627289748868856653701483607915443175041492575578772627945047164916971063680196281328125}{10830524179177118140004499218345942586606336379101385804}\cdot t^5+\frac{26085629682060700133836439328208572475254833041841586110129529979524912615708701351635455234375}{10830524179177118140004499218345942586606336379101385804}\cdot t^3-\frac{626857223464107267939842839050165807456308493211356266943681713189458130045065848652658203125}{10830524179177118140004499218345942586606336379101385804}\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 (probabilists') type can be downloaded here packed into a single file.