Rule: Q[8, 44]

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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{52}-\frac{14748961046415140680722505104276938864674798289072896}{96463059700968922754665093508150590981130145789}\cdot t^{50}+\frac{3348047648568943405709680729157200127290946729239721920}{79686875405148240536462468550211357767020555217}\cdot t^{48}-\frac{159531571650496850701862913500166464931011051023254828780800}{22604510323260384232176520245409955153244830829889}\cdot t^{46}+\frac{55072448697803368072398317303361908379299065330193882587099040}{67813530969781152696529560736229865459734492489667}\cdot t^{44}-\frac{354714092140733631066130167384179833246426315060844706633723040}{5216425459213934822809966210479220419979576345359}\cdot t^{42}+\frac{97103783456031657885157944364712431650859201369643576452774016360}{22604510323260384232176520245409955153244830829889}\cdot t^{40}-\frac{364342883263895416312181441451366409198431461456414743885920640400}{1738808486404644940936655403493073473326525448453}\cdot t^{38}+\frac{19814295124022451031281895361015854909360071327900900849707458825}{2473411787204331352683720346362835666182824251}\cdot t^{36}-\frac{599446874113649559988740660853629324930657653980617253613849885475}{2473411787204331352683720346362835666182824251}\cdot t^{34}+\frac{57718816390549484217613344471506469256565877316485796880038193356575}{9893647148817325410734881385451342664731297004}\cdot t^{32}-\frac{277005115533613314919279551706539496805130238022242689299795238739950}{2473411787204331352683720346362835666182824251}\cdot t^{30}+\frac{16954851881084099824806110176783011630535087725537068757673158428124375}{9893647148817325410734881385451342664731297004}\cdot t^{28}-\frac{206180405592701208174638843966773417606451243925480985754677162796862375}{9893647148817325410734881385451342664731297004}\cdot t^{26}+\frac{7926389030793746927557735013019473133280546507749840341919161374156648125}{39574588595269301642939525541805370658925188016}\cdot t^{24}-\frac{1298288830201894337298088611466638268825006192593802436340137610673438125}{860317143375419600933467946560986318672286696}\cdot t^{22}+\frac{242700615335770043078164873449080812154894313735079048675367602262491576875}{27530148588013427229870974289951562197513174272}\cdot t^{20}-\frac{1083557801268346726594798149042409312774697214617743422750309894687070978125}{27530148588013427229870974289951562197513174272}\cdot t^{18}+\frac{14516117195517555526899294246948703395260283277237680915763660054383019003125}{110120594352053708919483897159806248790052697088}\cdot t^{16}-\frac{8901729389369426954728059278783912279129212176044365173257715998297808253125}{27530148588013427229870974289951562197513174272}\cdot t^{14}+\frac{123991281108521042512162249019133885273589043530079820340452985532107639996875}{220241188704107417838967794319612497580105394176}\cdot t^{12}-\frac{146926346693802499523672947387840963611680987433573960323315597097963316659375}{220241188704107417838967794319612497580105394176}\cdot t^{10}+\frac{446783720175406579145274061460099760085457220171081882420466963484660582390625}{880964754816429671355871177278449990320421576704}\cdot t^8-\frac{99668596295593413358324595940440560123034846140447972283777889868481337703125}{440482377408214835677935588639224995160210788352}\cdot t^6+\frac{359536782402768037026341710124257477019255355903710296381842369480696379265625}{7047718038531437370846969418227599922563372613632}\cdot t^4-\frac{30335359591520212189801596960524336827884249437665394774015294237900646796875}{7047718038531437370846969418227599922563372613632}\cdot t^2+\frac{1543883273673835963592062164167340794728377833051342048147041636825187109375}{28190872154125749483387877672910399690253490454528}$

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.