Rule: Q[3, 46]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{49}-\frac{68478338013681585303329}{14954922734629214447}\cdot t^{47}+\frac{36002012880922200430827785}{29909845469258428894}\cdot t^{45}-\frac{1049744521963485120156187365}{5438153721683350708}\cdot t^{43}+\frac{230136019430467929332737421385}{10876307443366701416}\cdot t^{41}-\frac{36619922936539371217595349399885}{21752614886733402832}\cdot t^{39}+\frac{4383946027780527250040787569039805}{43505229773466805664}\cdot t^{37}-\frac{403912975364337496433699136924439875}{87010459546933611328}\cdot t^{35}+\frac{29060157006363246641411623582092511275}{174020919093867222656}\cdot t^{33}-\frac{823659069786780831576628299759274334175}{174020919093867222656}\cdot t^{31}+\frac{36962239333491148917740977311638327699175}{348041838187734445312}\cdot t^{29}-\frac{1314861705480925236533682536899543812440025}{696083676375468890624}\cdot t^{27}+\frac{37015312206554659157890157857317771155782125}{1392167352750937781248}\cdot t^{25}-\frac{820867373718282811088540804084397364562158125}{2784334705501875562496}\cdot t^{23}+\frac{14231886746381130226684386966465643040472598125}{5568669411003751124992}\cdot t^{21}-\frac{190813383347946095141762011627685471899006741875}{11137338822007502249984}\cdot t^{19}+\frac{1949190014635071173487511598684355121910556613125}{22274677644015004499968}\cdot t^{17}-\frac{29744991915823495282359067169565148206407658759375}{89098710576060017999872}\cdot t^{15}+\frac{165100504318667468768688034434386917696437401634375}{178197421152120035999744}\cdot t^{13}-\frac{643247755369075514444313568926958775090986837865625}{356394842304240071999488}\cdot t^{11}+\frac{1673964855774432589923536029825852534269594837178125}{712789684608480143998976}\cdot t^9-\frac{2706854373058127168786073848747260177781101491815625}{1425579369216960287997952}\cdot t^7+\frac{2428415857298262175080354753347919828777311296265625}{2851158738433920575995904}\cdot t^5-\frac{988267902903218679032175065684110844521710784734375}{5702317476867841151991808}\cdot t^3+\frac{115087853046551290677589703739075546522965125734375}{11404634953735682303983616}\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.