Rule: Q[5, 82]

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^{87}-\frac{685941644815778837977239467989063920959256970516889145238269876552679612422552163}{191625008585996880964174124244403232463212912198787653935971780272339489007279}\cdot t^{85}+\frac{45651071838691187612278155649301470360560475316573043404828657696536648783399156940545}{7473375334853878357602790845531726066065303575752718503502899430621240071283881}\cdot t^{83}-\frac{49459858866849525021302107011459004323025601427736039610968957592416710860649537067338385}{7473375334853878357602790845531726066065303575752718503502899430621240071283881}\cdot t^{81}+\frac{53766989899879918150275727433128113632889397964563581557450686227078487911526527462963150}{10511076420328942837697314831971485324986362272507339667373979508609339059471}\cdot t^{79}-\frac{2429479581740491313520753251276771323732496314309068081211891050062709706172179159560684990}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{77}+\frac{1128268116490901403559181042934489072854123526701948430528966358240215725523942140816435978430}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{75}-\frac{425495189888226837035141709294121860889527238857051567541702802710881207522268482668442376284750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{73}+\frac{132822916467267029531862309446186517215206218364984634755604086498319725631060067628069982816764875}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{71}-\frac{34810423939296127852801318872451507829448224097376158296011774331097891411342984341268508031973789375}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{69}+\frac{7742527292454350228341175346831154544774449315639452556822386076660235311948878101175209383433069248875}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{67}-\frac{1473671392804591819551773390949669428384413632610417240724750808842807482690601480803628313582449358580875}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{65}+\frac{241581918543634146644971394999538820729782846010617908228548208937084792120737105048975703039497884969785000}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{63}-\frac{34280600709068628571369031442285956592432996083904519592867258907911832640932248908753237072542932343503005000}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{61}+\frac{4226919991437824634487160476865822560235049260414506719658517948636469356882021992863524730414710047871229525000}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{59}-\frac{454200432841875002111363681602947165362850801205139473718769972681776492687200258225912160820915370081358919165000}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{57}+\frac{42620973642834617402023916604574655294618570371875108869081085015744222852699183109494520909156417183927033822173750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{55}-\frac{3497434534424076332403960930278290302055890375123435188990476557555371114569010301754823637180589022140523856618618750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{53}+\frac{251160161462179828080463431400628007556357561564349612014222041148082479230976629688918144297151930583593422018577043750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{51}-\frac{15787039694422721122250759875683789354800262465400736216940749772441057082131482333366948215579405296871147574328782343750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{49}+\frac{868235851010833576824628299338834433313615581572180341432432058043936148760887529513719260209929015865263161625441362562500}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{47}-\frac{41741984804489596236807546370922509678590714047122896795985944803367750000860848185947060640864879183709604962944352889812500}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{45}+\frac{1751838481164351024484299528082267732535266664927004786196926102881570877263104634487878390466253313842752982610857327772812500}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{43}-\frac{64056221986829072517356841606307460366812699473592342538216281842789683599094079707268073439289695665688029402942336974940312500}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{41}+\frac{2035641717030578502882083374556315000185669343533102819058257955173101757528463262731939347241216620067475936947737454003130468750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{39}-\frac{56052245085271455656650027497785183044045337933161507045497117557087420325985164337443548699945252325276898131160819572456592593750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{37}+\frac{1332440835223938746250525636415206893453036384946116814628933365013941079847379156296082572764111140260331498845971784947988140968750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{35}-\frac{27225958734469919758997038485854589293485255115682563025553971264083390526513501498610103145429530222338214176541757092472090772968750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{33}+\frac{475756395633462536879700418263738275286134607622889314724974594989758527088365798359157120199791148827100065408291493436293388080625000}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{31}-\frac{7067374632580678133063526654662871280695016495533708424260024066354845589999618133666975580745791815317273119700772993979020519303125000}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{29}+\frac{88626619666842332347510091373735936173885704089540666039565366168303163853951609627380465399312747485247118489462491350917032886208125000}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{27}-\frac{930530288914345329206747581596754210714459967543427951727728115864896990519420791148998329959930151332858520379016320809044009894613125000}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{25}+\frac{8100885888971938585275533221854971359748164697279243929819460842805738740436877428761113515460435862835908487615058362517520331194224609375}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{23}-\frac{57800054134120060230310640173703953775573656841804607179375901929057876017135909919382129946755470081860533569452267989657813315630544921875}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{21}+\frac{333292553207708070321447769341176119970563189929022646716741723335015668386412142197051680282786372228089160163087486315773741574292802734375}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{19}-\frac{1526675441405844105754230065751730343980067504186849847830116796827551459915483809662319924596475386454495643573765397965199911283208771484375}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{17}+\frac{5436643037226256056718617239754261662105167772680140941369830046150742068818498861900060348269987796443905004675560247379841774306454339843750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{15}-\frac{14641074312698767900048552142195476614318891364711863971640619895566429181385625394006606914142714469649109540975248725027885828391733261718750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{13}+\frac{28747823706823355474452216999093004503266200455523036720392301931532612653877166924165646068754601832501664049116279940406833828313316386718750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^{11}-\frac{39140137522349108052357130843542861571935036435759132493494971756849302669661812209725065997792918239194816715789258606634609082775087792968750}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^9+\frac{34359355617849844048890298685888877928404133051742647328476014578272772986427680208627967350264092758989515057423351560192057134996406240234375}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^7-\frac{17356918945046505445678061292970494970115212139620832691712279318776417190703539681616051549186869550588630438724678064161148893356667216796875}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^5+\frac{4123172041164797543135089981227245386436021484026848104028318257739642489943088144361301654132597361363787057339612318612751603034527490234375}{808544340025303295207485756305498871152797097885179974413383039123795312267}\cdot t^3-\frac{290363874159250046994523222457779159632592334317114862393005089491341150864210857677441620748100149946078383463414109337800568867875927734375}{808544340025303295207485756305498871152797097885179974413383039123795312267}\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.