Rule: Q[2, 71]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{73}-\frac{5885950926476709673862933153630584138051734298522}{1148596789480616685491341991404158861898656261}\cdot t^{71}+\frac{3562792415424148912806670352273914901360216563432895}{1148596789480616685491341991404158861898656261}\cdot t^{69}-\frac{39314628601445941994894592805688066612165656197635305}{33292660564655556101198318591424894547787138}\cdot t^{67}+\frac{10571604416236954005539292962434108870089028132430229475}{33292660564655556101198318591424894547787138}\cdot t^{65}-\frac{1068873348685925722392917655172402546345040395456856159185}{16646330282327778050599159295712447273893569}\cdot t^{63}+\frac{337966597296084278282273248152914604200367517103385231441735}{33292660564655556101198318591424894547787138}\cdot t^{61}-\frac{85752471836952359011991827595914041229246660776940246145116725}{66585321129311112202396637182849789095574276}\cdot t^{59}+\frac{35567762806809587196974214383696051391267063157960859158427368575}{266341284517244448809586548731399156382297104}\cdot t^{57}-\frac{6110003292604337034578222613681203905352365777895833637015174290875}{532682569034488897619173097462798312764594208}\cdot t^{55}+\frac{878029512148964430024613154683065742552025794833321325115480440335825}{1065365138068977795238346194925596625529188416}\cdot t^{53}-\frac{106321911973367515340998947836463944337219311302952313397721630263719075}{2130730276137955590476692389851193251058376832}\cdot t^{51}+\frac{170416155241812943890065862297869469967118840177013315417193225526668125}{66585321129311112202396637182849789095574276}\cdot t^{49}-\frac{475672312121821068308692907223366374241342762571598799387459390408715426875}{4261460552275911180953384779702386502116753664}\cdot t^{47}+\frac{35366396095368933848082509228005736732014019668237034054153588523643930453125}{8522921104551822361906769559404773004233507328}\cdot t^{45}-\frac{2244270228828453129407462349614021724581361972033482213641296708828126616539375}{17045842209103644723813539118809546008467014656}\cdot t^{43}+\frac{486346389693097158057963904608059334209842044326219530569184071827866425581191875}{136366737672829157790508312950476368067736117248}\cdot t^{41}-\frac{22479999746300014009694024159318686856368360661295410009132543384881310548968721875}{272733475345658315581016625900952736135472234496}\cdot t^{39}+\frac{885121961774388424121082408339627398714902795840454407207966249394286079931614940625}{545466950691316631162033251801905472270944468992}\cdot t^{37}-\frac{29613068423114626148710563554333855660378904200460474430559163274205166691991350171875}{1090933901382633262324066503603810944541888937984}\cdot t^{35}+\frac{419479206913532626836690152645716219990016438243045340698213021029348781593978124821875}{1090933901382633262324066503603810944541888937984}\cdot t^{33}-\frac{5009261978703528099227905596146148236972415361767602704754792425032974622960496084809375}{1090933901382633262324066503603810944541888937984}\cdot t^{31}+\frac{100293547626352031401404573926290372082460723066244664068719622509374757484722367820765625}{2181867802765266524648133007207621889083777875968}\cdot t^{29}-\frac{1671828786240540749212361682060908856172047550804918901764723467560267566478988780432796875}{4363735605530533049296266014415243778167555751936}\cdot t^{27}+\frac{46017809002169740398167505458751806622357724471079559746798067325750438182072127174644609375}{17454942422122132197185064057660975112670223007744}\cdot t^{25}-\frac{517615512081643966582481180606664350420196696973382899403735678704356600535605990259558921875}{34909884844244264394370128115321950225340446015488}\cdot t^{23}+\frac{4700130037797096740073035800546218323351595275935930911808127731670234982701755883427530015625}{69819769688488528788740256230643900450680892030976}\cdot t^{21}-\frac{33938045378698792673889353014718842098538988465846911839920624245408119408328244992219746796875}{139639539376977057577480512461287800901361784061952}\cdot t^{19}+\frac{47818201511114718126544831395601550246809931592186211933464675078644324202276111271254807890625}{69819769688488528788740256230643900450680892030976}\cdot t^{17}-\frac{411004007085948060703873737638734134775366404102601587802877970532394992326390263687465539453125}{279279078753954115154961024922575601802723568123904}\cdot t^{15}+\frac{1307271917236767057462609974208632880152976729554029260804339908386440924196219503390376806796875}{558558157507908230309922049845151203605447136247808}\cdot t^{13}-\frac{2959042746918446464258375019392655177748043273884462297267462572675514557080829049749054502890625}{1117116315015816460619844099690302407210894272495616}\cdot t^{11}+\frac{36146284210049772311342435699789670163423849952897023426059912627787686087450366049189994787890625}{17873861040253063369917505595044838515374308359929856}\cdot t^9-\frac{34478978890877351715416961690469452690340478061690207561482416234131324016406544724724171084765625}{35747722080506126739835011190089677030748616719859712}\cdot t^7+\frac{18236429483028860615145300814571899095600242450189374304913845769963034228722811279215744263671875}{71495444161012253479670022380179354061497233439719424}\cdot t^5-\frac{4336291160819648200051464368832190184904760061490614234815216566728811119400115359390445522265625}{142990888322024506959340044760358708122994466879438848}\cdot t^3+\frac{144257245746531866490654163895874192842060452145772920699912740442126709608071383768063980859375}{142990888322024506959340044760358708122994466879438848}\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.