Rule: Q[18, 33]

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.

• $P_1$:
  $262144\cdot t^{18}-20054016\cdot t^{16}+601620480\cdot t^{14}-9124577280\cdot t^{12}+75277762560\cdot t^{10}-338749931520\cdot t^8+790416506880\cdot t^6-846874828800\cdot t^4+317578060800\cdot t^2-17643225600$
• $P_2$:
  $262144\cdot t^{51}-\frac{9377899897872178789675982782464}{72793935863433752742211}\cdot t^{49}+\frac{23309105506324942114427476559265792}{800733294497771280164321}\cdot t^{47}-\frac{3218170169452052701831647337503129600}{800733294497771280164321}\cdot t^{45}+\frac{304315578526503618173541244219550760960}{800733294497771280164321}\cdot t^{43}-\frac{397848955032224449937625907522299881963520}{15213932595457654323122099}\cdot t^{41}+\frac{20658296019918448602236412067514496219463680}{15213932595457654323122099}\cdot t^{39}-\frac{828536328421686393144159881732042852179107840}{15213932595457654323122099}\cdot t^{37}+\frac{26058548470743939138671380214002759544425190400}{15213932595457654323122099}\cdot t^{35}-\frac{58992857285035782956091377062891106471355993600}{1383084781405241302102009}\cdot t^{33}+\frac{1169635970560435540094054827169241824718561945600}{1383084781405241302102009}\cdot t^{31}-\frac{18505382219964982898522706753352656212403650688000}{1383084781405241302102009}\cdot t^{29}+\frac{8052058499155667638500448268650465933139247456000}{47692578669146251796621}\cdot t^{27}-\frac{4251561444256463471045490242083005969515832336000}{2510135719428750094559}\cdot t^{25}+\frac{640594848885418170519088482441073327659733126800000}{47692578669146251796621}\cdot t^{23}-\frac{173107099023598232002361343168830679165247640760000}{2073590376919402252027}\cdot t^{21}+\frac{833437376885257282046923832177971244110144867972500}{2073590376919402252027}\cdot t^{19}-\frac{161081907615290683929330603152816489257875342738750}{109136335627336960633}\cdot t^{17}+\frac{442095779148545398551956792518935280456796964862500}{109136335627336960633}\cdot t^{15}-\frac{882858764004159468455349521307497959856396393981250}{109136335627336960633}\cdot t^{13}+\frac{2475068440079125829428484766974657790049160499178125}{218272671254673921266}\cdot t^{11}-\frac{4634105630149329197884358045032282862136099095353125}{436545342509347842532}\cdot t^9+\frac{2695359896375877566306290269943450239478506400715625}{436545342509347842532}\cdot t^7-\frac{1739658971115747863353666118650759326721184071640625}{873090685018695685064}\cdot t^5+\frac{2038130691576074271044873485498626291159256795640625}{6984725480149565480512}\cdot t^3-\frac{170915607399458308193589906631238400147868030265625}{13969450960299130961024}\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.