Rule: Q[17, 32]

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.

• $P_1$:
  $131072\cdot t^{17}-8912896\cdot t^{15}+233963520\cdot t^{13}-3041525760\cdot t^{11}+20910489600\cdot t^9-75277762560\cdot t^7+131736084480\cdot t^5-94097203200\cdot t^3+17643225600\cdot t$
• $P_2$:
  $131072\cdot t^{49}-\frac{10995366054413596512374751232}{182562970566544874259}\cdot t^{47}+\frac{25460605223773249980327802568704}{2008192676231993616849}\cdot t^{45}-\frac{1087352705943240268760751418245120}{669397558743997872283}\cdot t^{43}+\frac{12393175431314563629766721734819840}{87312725053564939863}\cdot t^{41}-\frac{342780941701801069842205800544717864960}{38155660848407878720131}\cdot t^{39}+\frac{5430166255376623658145175359751641620480}{12718553616135959573377}\cdot t^{37}-\frac{594719149612070542464755937847285091655680}{38155660848407878720131}\cdot t^{35}+\frac{16923126761098128661042094594858691372505600}{38155660848407878720131}\cdot t^{33}-\frac{11476478242871936059608533333064412772454400}{1156232146921450870307}\cdot t^{31}+\frac{202939759401224484745226014180539552068224000}{1156232146921450870307}\cdot t^{29}-\frac{2839129970067804465171448906720214603272832000}{1156232146921450870307}\cdot t^{27}+\frac{31367475782669299975248439340558885273191056000}{1156232146921450870307}\cdot t^{25}-\frac{11843220949532344737358998594180102912909600000}{50270962909628298709}\cdot t^{23}+\frac{80214117694591651093439783843434827755823000000}{50270962909628298709}\cdot t^{21}-\frac{22056283580038635078851850809589226858019640000}{2645840153138331511}\cdot t^{19}+\frac{87559588974367194093713947982413981777402691250}{2645840153138331511}\cdot t^{17}-\frac{258911346189438302106124740171571572672597645000}{2645840153138331511}\cdot t^{15}+\frac{555354361348257116793522957204148767407229131250}{2645840153138331511}\cdot t^{13}-\frac{833784270520982513820900479972519487250697606250}{2645840153138331511}\cdot t^{11}+\frac{3335353325699124195227542960106544045686516634375}{10583360612553326044}\cdot t^9-\frac{1033694733998729520489300822394655059874965471875}{5291680306276663022}\cdot t^7+\frac{1419110592087224202011879841510720254395261228125}{21166721225106652088}\cdot t^5-\frac{220873332794455029344786075548737878159525484375}{21166721225106652088}\cdot t^3+\frac{158205616476766585577348697879052420862924484375}{338667539601706433408}\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.