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.

• $P_1$:
  $t^{18}-153\cdot t^{16}+9180\cdot t^{14}-278460\cdot t^{12}+4594590\cdot t^{10}-41351310\cdot t^8+192972780\cdot t^6-413513100\cdot t^4+310134825\cdot t^2-34459425$
• $P_2$:
  $t^{51}-\frac{71547698195435934369476187}{72793935863433752742211}\cdot t^{49}+\frac{355668724156569551306571602772}{800733294497771280164321}\cdot t^{47}-\frac{98210759565797506769764628219700}{800733294497771280164321}\cdot t^{45}+\frac{18573948884674293101412429456759690}{800733294497771280164321}\cdot t^{43}-\frac{48565546268582086174026600039343247310}{15213932595457654323122099}\cdot t^{41}+\frac{5043529301737902490780374039920531303580}{15213932595457654323122099}\cdot t^{39}-\frac{404558754112151559152421817251974048915580}{15213932595457654323122099}\cdot t^{37}+\frac{25447801240960878065108769740237069867602725}{15213932595457654323122099}\cdot t^{35}-\frac{115220424384835513586115970825959192326867175}{1383084781405241302102009}\cdot t^{33}+\frac{4568890510001701328492401668629850877806882600}{1383084781405241302102009}\cdot t^{31}-\frac{144573298593476428894708646510567626659403521000}{1383084781405241302102009}\cdot t^{29}+\frac{125813414049307306851569504197663530205300741500}{47692578669146251796621}\cdot t^{27}-\frac{132861295133014483470171570065093936547369760500}{2510135719428750094559}\cdot t^{25}+\frac{40037178055338635657443030152567082978733320425000}{47692578669146251796621}\cdot t^{23}-\frac{21638387377949779000295167896103834895655955095000}{2073590376919402252027}\cdot t^{21}+\frac{208359344221314320511730958044492811027536216993125}{2073590376919402252027}\cdot t^{19}-\frac{80540953807645341964665301576408244628937671369375}{109136335627336960633}\cdot t^{17}+\frac{442095779148545398551956792518935280456796964862500}{109136335627336960633}\cdot t^{15}-\frac{1765717528008318936910699042614995919712792787962500}{109136335627336960633}\cdot t^{13}+\frac{4950136880158251658856969533949315580098320998356250}{109136335627336960633}\cdot t^{11}-\frac{9268211260298658395768716090064565724272198190706250}{109136335627336960633}\cdot t^9+\frac{10781439585503510265225161079773800957914025602862500}{109136335627336960633}\cdot t^7-\frac{6958635884462991453414664474603037306884736286562500}{109136335627336960633}\cdot t^5+\frac{2038130691576074271044873485498626291159256795640625}{109136335627336960633}\cdot t^3-\frac{170915607399458308193589906631238400147868030265625}{109136335627336960633}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.