Rule: Q[4, 5, 40]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^9-168\cdot t^7+432\cdot t^5-270\cdot t^3+45\cdot t$
• $P_3$:
  $16\cdot t^{49}-\frac{568606710067804714700476221573369771702597180884558110248614464086072}{65703617067213487295636604494416823944702401140119109814307960999}\cdot t^{47}+\frac{140988920027455025077213440720422220659109547191467721423592878502471608}{65703617067213487295636604494416823944702401140119109814307960999}\cdot t^{45}-\frac{21283089217432653424187489545297441753141791043543114192409814447994905270}{65703617067213487295636604494416823944702401140119109814307960999}\cdot t^{43}+\frac{2190866337377804835732821457129749276782195289549583405267133083356091326670}{65703617067213487295636604494416823944702401140119109814307960999}\cdot t^{41}-\frac{326512641058774678259835041767286700987777437693488097786365172353724125384605}{131407234134426974591273208988833647889404802280238219628615921998}\cdot t^{39}+\frac{493227929090320000605583106148068082849462934213128978902934686979146222590395}{3551546868498026340304681324022531024037967629195627557530160054}\cdot t^{37}-\frac{84571802597664457643962603268802089329563182035713047649233017831823366460174645}{14206187473992105361218725296090124096151870516782510230120640216}\cdot t^{35}+\frac{5639455172878922191512496550325821538147144392540386318809662753952919961556355425}{28412374947984210722437450592180248192303741033565020460241280432}\cdot t^{33}-\frac{147471817968208848401154044546068008924624608874015557195018700703931381457072884175}{28412374947984210722437450592180248192303741033565020460241280432}\cdot t^{31}+\frac{3036912808085764712905509198069868947994890789901462946379985595225692185597283040475}{28412374947984210722437450592180248192303741033565020460241280432}\cdot t^{29}-\frac{197101500567282170476054902116155405897036064597206162366551997987891029174200246451075}{113649499791936842889749802368720992769214964134260081840965121728}\cdot t^{27}+\frac{2513069048121013793407268430512171841438234556243567727050010249172751787528137822051425}{113649499791936842889749802368720992769214964134260081840965121728}\cdot t^{25}-\frac{100137028357814548302903702390514302169548081464775052755049360182064400801345160773450625}{454597999167747371558999209474883971076859856537040327363860486912}\cdot t^{23}+\frac{772378185457984384665346731493756325386182049393163916784672874309414252213425052464344375}{454597999167747371558999209474883971076859856537040327363860486912}\cdot t^{21}-\frac{18219593973584283523571783921665066258749782637321758380706327673281114720090522333219008125}{1818391996670989486235996837899535884307439426148161309455441947648}\cdot t^{19}+\frac{323065995819006626062791227920677318873709028774490873010087976167189141875662334018667888125}{7273567986683957944943987351598143537229757704592645237821767790592}\cdot t^{17}-\frac{2105440655924597911646331306369769824762021121286630299508007141526541990330428303860392964375}{14547135973367915889887974703196287074459515409185290475643535581184}\cdot t^{15}+\frac{4896861103492076054164006875673143829058460000677563329500895232959549261596681439628747509375}{14547135973367915889887974703196287074459515409185290475643535581184}\cdot t^{13}-\frac{31272534244881653502844728613574178673583694603509767212330012670958568597362697986331281896875}{58188543893471663559551898812785148297838061636741161902574142324736}\cdot t^{11}+\frac{32516347475659728527717043401302002506294026499003337074506971836276366490384060663548639371875}{58188543893471663559551898812785148297838061636741161902574142324736}\cdot t^9-\frac{81876859482016365071696571275437591729408488303762422869781462253045911862077872937481706603125}{232754175573886654238207595251140593191352246546964647610296569298944}\cdot t^7+\frac{28063433349625435974807696102826575766373094865662590008570852411750318022394925759666924584375}{232754175573886654238207595251140593191352246546964647610296569298944}\cdot t^5-\frac{17629554654081322429842161044166187705560806342082522980550821946313475900017682675662359390625}{931016702295546616952830381004562372765408986187858590441186277195776}\cdot t^3+\frac{1720857074793974401419103100413461467137947217272018577471470745435319462667255339252903234375}{1862033404591093233905660762009124745530817972375717180882372554391552}\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.