Rule: Q[5, 60]

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.

• $P_1$:
  $32\cdot t^5-160\cdot t^3+120\cdot t$
• $P_2$:
  $32\cdot t^{65}-\frac{8655296520517891654795166862986953258392398387569269760}{274964871045848058956059254065666169824960138389627}\cdot t^{63}+\frac{27935579333661626399594049416769451697075921845073497393740}{1924754097320936412692414778459663188774720968727389}\cdot t^{61}-\frac{8032806743202586904099023813551128135559083023965983892881700}{1924754097320936412692414778459663188774720968727389}\cdot t^{59}+\frac{85097094277150605756633799213601040470231807659950307615399725}{101302847227417705931179725182087536251301103617231}\cdot t^{57}-\frac{1822529959603467853656731379724853392496772948807116239930604430}{14471835318202529418739960740298219464471586231033}\cdot t^{55}+\frac{845741398043641797795961083682512292432262420987900635278247400475}{57887341272810117674959842961192877857886344924132}\cdot t^{53}-\frac{77874029140105640864836754106527501753747665556734964975071426906575}{57887341272810117674959842961192877857886344924132}\cdot t^{51}+\frac{23168120513827813516300943433791615722865423195363918490054141954129375}{231549365091240470699839371844771511431545379696528}\cdot t^{49}-\frac{352337806089264350560381207630793160959144561153696277977623498082431875}{57887341272810117674959842961192877857886344924132}\cdot t^{47}+\frac{6580668998367972128146697657780441805729066900077058729427711448713016625}{21539475822440974018589709008815954551771663227584}\cdot t^{45}-\frac{11792355456179989254407530747869721845292527344198369644992410947670651338125}{926197460364961882799357487379086045726181518786112}\cdot t^{43}+\frac{38107513131742953590085825957237766269272464468267595775492973771130839738125}{86157903289763896074358836035263818207086652910336}\cdot t^{41}-\frac{553033039910857176273434042754757586162840167973524322409007333892170382896875}{43078951644881948037179418017631909103543326455168}\cdot t^{39}+\frac{107374694902202107225004924821102333325285311008393377531826924122189610645928125}{344631613159055584297435344141055272828346611641344}\cdot t^{37}-\frac{2177681343212744969340659359861483257442659483652051169864058436557483510663748125}{344631613159055584297435344141055272828346611641344}\cdot t^{35}+\frac{147349982747406991232557299848507337914547278161622354274673712817988396879090753125}{1378526452636222337189741376564221091313386446565376}\cdot t^{33}-\frac{259038045571946960075233923545008706898187342883135871402132199194987712090587684375}{172315806579527792148717672070527636414173305820672}\cdot t^{31}+\frac{96480234546382193524797164860196558914391561487107767222655241937935815003400038109375}{5514105810544889348758965506256884365253545786261504}\cdot t^{29}-\frac{923759183759587325986172109917649701647197772025002281472195246428095069752712446453125}{5514105810544889348758965506256884365253545786261504}\cdot t^{27}+\frac{28879595696569997440970318832828229330643321227342515436526212337342453089797520018621875}{22056423242179557395035862025027537461014183145046016}\cdot t^{25}-\frac{91244844167297092961844148860399596803352428671464340062435802458684977952619011463046875}{11028211621089778697517931012513768730507091572523008}\cdot t^{23}+\frac{3685064823556891863317955006102078504044017990013155905131816247618326147570965558591171875}{88225692968718229580143448100110149844056732580184064}\cdot t^{21}-\frac{14644811008787761555859656947880501175951576807664531038778456660547161815235299790343359375}{88225692968718229580143448100110149844056732580184064}\cdot t^{19}+\frac{179927400416269950615733274610954397617806149036948193059381631465711986084992255617471484375}{352902771874872918320573792400440599376226930320736256}\cdot t^{17}-\frac{104343293203206976319988405816615574735394210755648373747169073117479759333453989058212015625}{88225692968718229580143448100110149844056732580184064}\cdot t^{15}+\frac{2839400354072702188897134883750304613349855719160988271521185631176715864475021899002844296875}{1411611087499491673282295169601762397504907721282945024}\cdot t^{13}-\frac{3405703325742365899961810262912759079299233740012666178405844603830529464471957339123738203125}{1411611087499491673282295169601762397504907721282945024}\cdot t^{11}+\frac{10930839303456732692465603882102092170726411545825133857772552752603675920989855733986887109375}{5646444349997966693129180678407049590019630885131780096}\cdot t^9-\frac{2720588845175403106823057805149289178128985959613788023258604507603953415007264720776664453125}{2823222174998983346564590339203524795009815442565890048}\cdot t^7+\frac{5983745537651497564410911857786614639169945074441123947598954680507157560402081691897823359375}{22585777399991866772516722713628198360078523540527120384}\cdot t^5-\frac{741421410111578170922055996229373484526528435312860924311353328795396490924114492271327734375}{22585777399991866772516722713628198360078523540527120384}\cdot t^3+\frac{104541846218104535837360921701346146979176039125436929874548402077539464072660051372819140625}{90343109599967467090066890854512793440314094162108481536}\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.