Rule: Q[1, 2, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^{47}-\frac{3514153654452277745561}{3361510671905005977}\cdot t^{45}+\frac{560094854974915264947525}{2241007114603337318}\cdot t^{43}-\frac{23235237349503802180731855}{640287747029524948}\cdot t^{41}+\frac{4589211166692680833587627675}{1280575494059049896}\cdot t^{39}-\frac{654332443892435585022558356115}{2561150988118099792}\cdot t^{37}+\frac{69768361009792761626324762278245}{5122301976236199584}\cdot t^{35}-\frac{5686994763539639731787371497356625}{10244603952472399168}\cdot t^{33}+\frac{179641401761147525936125560635060025}{10244603952472399168}\cdot t^{31}-\frac{8866618776816825270702172862629823625}{20489207904944798336}\cdot t^{29}+\frac{343141664249892418409003718753397432575}{40978415809889596672}\cdot t^{27}-\frac{10411891887501693410950202360790221192475}{81956831619779193344}\cdot t^{25}+\frac{246861130393920491316691242397596289546875}{163913663239558386688}\cdot t^{23}-\frac{4542808906990427521691210670860428728331875}{327827326479116773376}\cdot t^{21}+\frac{64219806452410651454825299748976098863003125}{655654652958233546752}\cdot t^{19}-\frac{687391264019599746960819809559521741531720625}{1311309305916467093504}\cdot t^{17}+\frac{10925504486189207144722730433672171252428495625}{5245237223665868374016}\cdot t^{15}-\frac{62786031519102820709806472412200567904462515625}{10490474447331736748032}\cdot t^{13}+\frac{251727692309709392180155564004512495180539909375}{20980948894663473496064}\cdot t^{11}-\frac{669791682913080396700696637662556444875218796875}{41961897789326946992128}\cdot t^9+\frac{1099616293294393121499592062088006516136395509375}{83923795578653893984256}\cdot t^7-\frac{993607557345241528937930176383411431497397184375}{167847591157307787968512}\cdot t^5+\frac{403454009725495425625576495763098339481090390625}{335695182314615575937024}\cdot t^3-\frac{46339333129265119198494450887799679578225328125}{671390364629231151874048}\cdot t$

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.