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.

• $P_1$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_2$:
  $t^{65}-\frac{540956032532368228424697928936684578649524899223079360}{274964871045848058956059254065666169824960138389627}\cdot t^{63}+\frac{6983894833415406599898512354192362924268980461268374348435}{3849508194641872825384829556919326377549441937454778}\cdot t^{61}-\frac{2008201685800646726024755953387782033889770755991495973220425}{1924754097320936412692414778459663188774720968727389}\cdot t^{59}+\frac{85097094277150605756633799213601040470231807659950307615399725}{202605694454835411862359450364175072502602207234462}\cdot t^{57}-\frac{1822529959603467853656731379724853392496772948807116239930604430}{14471835318202529418739960740298219464471586231033}\cdot t^{55}+\frac{845741398043641797795961083682512292432262420987900635278247400475}{28943670636405058837479921480596438928943172462066}\cdot t^{53}-\frac{77874029140105640864836754106527501753747665556734964975071426906575}{14471835318202529418739960740298219464471586231033}\cdot t^{51}+\frac{23168120513827813516300943433791615722865423195363918490054141954129375}{28943670636405058837479921480596438928943172462066}\cdot t^{49}-\frac{1409351224357057402241524830523172643836578244614785111910493992329727500}{14471835318202529418739960740298219464471586231033}\cdot t^{47}+\frac{6580668998367972128146697657780441805729066900077058729427711448713016625}{673108619451280438080928406525498579742864475862}\cdot t^{45}-\frac{11792355456179989254407530747869721845292527344198369644992410947670651338125}{14471835318202529418739960740298219464471586231033}\cdot t^{43}+\frac{38107513131742953590085825957237766269272464468267595775492973771130839738125}{673108619451280438080928406525498579742864475862}\cdot t^{41}-\frac{1106066079821714352546868085509515172325680335947048644818014667784340765793750}{336554309725640219040464203262749289871432237931}\cdot t^{39}+\frac{107374694902202107225004924821102333325285311008393377531826924122189610645928125}{673108619451280438080928406525498579742864475862}\cdot t^{37}-\frac{2177681343212744969340659359861483257442659483652051169864058436557483510663748125}{336554309725640219040464203262749289871432237931}\cdot t^{35}+\frac{147349982747406991232557299848507337914547278161622354274673712817988396879090753125}{673108619451280438080928406525498579742864475862}\cdot t^{33}-\frac{2072304364575575680601871388360069655185498743065086971217057593559901696724701475000}{336554309725640219040464203262749289871432237931}\cdot t^{31}+\frac{96480234546382193524797164860196558914391561487107767222655241937935815003400038109375}{673108619451280438080928406525498579742864475862}\cdot t^{29}-\frac{923759183759587325986172109917649701647197772025002281472195246428095069752712446453125}{336554309725640219040464203262749289871432237931}\cdot t^{27}+\frac{28879595696569997440970318832828229330643321227342515436526212337342453089797520018621875}{673108619451280438080928406525498579742864475862}\cdot t^{25}-\frac{182489688334594185923688297720799193606704857342928680124871604917369955905238022926093750}{336554309725640219040464203262749289871432237931}\cdot t^{23}+\frac{3685064823556891863317955006102078504044017990013155905131816247618326147570965558591171875}{673108619451280438080928406525498579742864475862}\cdot t^{21}-\frac{14644811008787761555859656947880501175951576807664531038778456660547161815235299790343359375}{336554309725640219040464203262749289871432237931}\cdot t^{19}+\frac{179927400416269950615733274610954397617806149036948193059381631465711986084992255617471484375}{673108619451280438080928406525498579742864475862}\cdot t^{17}-\frac{417373172812827905279953623266462298941576843022593494988676292469919037333815956232848062500}{336554309725640219040464203262749289871432237931}\cdot t^{15}+\frac{2839400354072702188897134883750304613349855719160988271521185631176715864475021899002844296875}{673108619451280438080928406525498579742864475862}\cdot t^{13}-\frac{3405703325742365899961810262912759079299233740012666178405844603830529464471957339123738203125}{336554309725640219040464203262749289871432237931}\cdot t^{11}+\frac{10930839303456732692465603882102092170726411545825133857772552752603675920989855733986887109375}{673108619451280438080928406525498579742864475862}\cdot t^9-\frac{5441177690350806213646115610298578356257971919227576046517209015207906830014529441553328906250}{336554309725640219040464203262749289871432237931}\cdot t^7+\frac{5983745537651497564410911857786614639169945074441123947598954680507157560402081691897823359375}{673108619451280438080928406525498579742864475862}\cdot t^5-\frac{741421410111578170922055996229373484526528435312860924311353328795396490924114492271327734375}{336554309725640219040464203262749289871432237931}\cdot t^3+\frac{104541846218104535837360921701346146979176039125436929874548402077539464072660051372819140625}{673108619451280438080928406525498579742864475862}\cdot t$

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.