Rule: Q[8, 55]

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.

• $P_1$:
  $t^8-28\cdot t^6+210\cdot t^4-420\cdot t^2+105$
• $P_2$:
  $t^{63}-\frac{203652374172493620481907533971596847159924749536990451071935693490079261}{118177038338135243199369522458882662745162641370259576393835461404150}\cdot t^{61}+\frac{163820008783103278697399496810637811956703308699100144176399035537002485023}{118177038338135243199369522458882662745162641370259576393835461404150}\cdot t^{59}-\frac{8182172408895330629348826678004997583840411523558547808572273281992246302523}{11817703833813524319936952245888266274516264137025957639383546140415}\cdot t^{57}+\frac{133825015127435553273415732079249539492776168007423759989886174041542560362026424}{555432080189235643037036755556748514902264414440220009051026668599505}\cdot t^{55}-\frac{69031747221043374851778952429975185792314229589083989558818730351019204498980183697}{1110864160378471286074073511113497029804528828880440018102053337199010}\cdot t^{53}+\frac{2741099217542940782857788544811146938886463325079763980938369602530527906214625913699}{222172832075694257214814702222699405960905765776088003620410667439802}\cdot t^{51}-\frac{214766389030923717333815058741479691817587162196193641225939550396283568105017049350672}{111086416037847128607407351111349702980452882888044001810205333719901}\cdot t^{49}+\frac{27023150558818869523499420972841968977168477147280160698075743098541363303087572779813415}{111086416037847128607407351111349702980452882888044001810205333719901}\cdot t^{47}-\frac{117590028668036023119516451658977992880152340922018069244836273880554471689037758200373845}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{45}+\frac{9855031080040201247962050454807049083013530745051005961879040785907406855978124206138512255}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{43}-\frac{340382270181901252245639471682766087019366852051623443704824275074553426329519992324134066845}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^{41}+\frac{19448473978698975177293506341519792398510077428888796526958695794343623698334050090466769403810}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^{39}-\frac{1841455342953920351243674904475507789993336159449423087643376345489352655625178252366126748182475}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{37}+\frac{72243323561204440308305510709084897684747111021760085044222118147127537963705818643686298456433725}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{35}-\frac{1172815365503883020794515742979528327018171807945192381516581855685322236026008300030117463906332450}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^{33}+\frac{31429876043726289206216508399499801400761451286022227246049298336425344958821441916865849423301617925}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^{31}-\frac{1384661998333861451322603844730564900905629738992953743350726448387454455969181807919020639736464637175}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{29}+\frac{24929899079386707381392754213704672773026038817908628069686133675761194729928977073371620775742184610125}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{27}-\frac{182089361392188714133695666033341623619767289310675222870005663119241470050289210001427302292557162405625}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^{25}+\frac{2138206326831501360735744287820378073734484729676288427750468515129717426646531122090660108253134714482500}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^{23}-\frac{39895748112248222480819537868978507833880568508273716765453289678386544671308432591250348425256898661170625}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{21}+\frac{291372791863457340286504500604287553308148083357328280665976875361709065843410916578092963208182054061299375}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{19}-\frac{817492427122830078583102024509746756261719171347620683010401190372090535309807539321034739271728882782187500}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^{17}+\frac{3440472874580129688789692855014381375905600464573021640553311796943611182240778315224562055098097950389009375}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^{15}-\frac{21042953272370771358371803243839017818956591269010561976478481002249895464521054793161992154801184449130559375}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{13}+\frac{44815021655985573888175974825297652559553840458832364084454724121141423665414082273681045998673862029190488125}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^{11}-\frac{31339232059946579295499564543190353005348649016691024435227733427385860588312281147697561278687146774972236875}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^9+\frac{26483622537802195392397224769808426038610231625937535418574371639092867398117756128386788138266659605443431250}{2363540766762704863987390449177653254903252827405191527876709228083}\cdot t^7-\frac{23955044338674042390903969763221746184153961095035305259995985646779372146541060630059213740363791842046090625}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^5+\frac{4844846093644958118700695677551590455457804346061496377184576013904719717065855779336311731939027785915034375}{4727081533525409727974780898355306509806505654810383055753418456166}\cdot t^3-\frac{159566292152745665819956607591852041305405698887364127703677763164702672074335856724522036396833853909281250}{2363540766762704863987390449177653254903252827405191527876709228083}\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.