Rule: Q[1, 60]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{61}-1830\cdot t^{59}+\frac{1565565}{2}\cdot t^{57}-208220145\cdot t^{55}+\frac{309206915325}{8}\cdot t^{53}-\frac{42608712931785}{8}\cdot t^{51}+\frac{18108702996008625}{32}\cdot t^{49}-\frac{380282762916181125}{8}\cdot t^{47}+\frac{411085666712391796125}{128}\cdot t^{45}-\frac{22609711669181548786875}{128}\cdot t^{43}+\frac{4083313927454187710909625}{512}\cdot t^{41}-\frac{76098123193464407339679375}{256}\cdot t^{39}+\frac{18796236428785708612900805625}{2048}\cdot t^{37}-\frac{481472825445049305238151405625}{2048}\cdot t^{35}+\frac{40925190162829190945242869478125}{8192}\cdot t^{33}-\frac{90035418358224220079534312851875}{1024}\cdot t^{31}+\frac{41866469536574262336983455476121875}{32768}\cdot t^{29}-\frac{499934900936739720847508321273690625}{32768}\cdot t^{27}+\frac{19497461136532849113052824529673934375}{131072}\cdot t^{25}-\frac{76963662381050720183103254722397109375}{65536}\cdot t^{23}+\frac{3894361316481166441265024688953293734375}{524288}\cdot t^{21}-\frac{19471806582405832206325123444766468671875}{524288}\cdot t^{19}+\frac{302698084144672482480145100823187831171875}{2097152}\cdot t^{17}-\frac{223733366541714443572281161478008396953125}{524288}\cdot t^{15}+\frac{7830667828960005525029840651730293893359375}{8388608}\cdot t^{13}-\frac{12215841813177608619046551416699258473640625}{8388608}\cdot t^{11}+\frac{51682407671136036465196948301419939696171875}{33554432}\cdot t^9-\frac{17227469223712012155065649433806646565390625}{16777216}\cdot t^7+\frac{51682407671136036465196948301419939696171875}{134217728}\cdot t^5-\frac{8910759943299316631930508327831024085546875}{134217728}\cdot t^3+\frac{1782151988659863326386101665566204817109375}{536870912}\cdot t$

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.