Rule: Q[18, 27]

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.

• $P_1$:
  $t^{18}-153\cdot t^{16}+9180\cdot t^{14}-278460\cdot t^{12}+4594590\cdot t^{10}-41351310\cdot t^8+192972780\cdot t^6-413513100\cdot t^4+310134825\cdot t^2-34459425$
• $P_2$:
  $t^{45}-\frac{1720120189237890201549207}{2416372265418801343709}\cdot t^{43}+\frac{553826243029276288441856700}{2416372265418801343709}\cdot t^{41}-\frac{107047962190612625020137401778}{2416372265418801343709}\cdot t^{39}+\frac{13905211321597740341907599210529}{2416372265418801343709}\cdot t^{37}-\frac{1287779773533707508982854092851815}{2416372265418801343709}\cdot t^{35}+\frac{8003885392729257892886234597259690}{219670205947163758519}\cdot t^{33}-\frac{412738262975160688353014415312731880}{219670205947163758519}\cdot t^{31}+\frac{16265589315281415032970705980080171230}{219670205947163758519}\cdot t^{29}-\frac{493443736381419757771116607975098032490}{219670205947163758519}\cdot t^{27}+\frac{11554554870342646187936092478471582643600}{219670205947163758519}\cdot t^{25}-\frac{208592146393198854584171835160243757758500}{219670205947163758519}\cdot t^{23}+\frac{2889042254146251062472815382156252284940750}{219670205947163758519}\cdot t^{21}-\frac{30433136606636819659133671583109188427611250}{219670205947163758519}\cdot t^{19}+\frac{240677985100360857325970573972669728183987500}{219670205947163758519}\cdot t^{17}-\frac{1403194256003837147092416283306941074326905000}{219670205947163758519}\cdot t^{15}+\frac{5882227567693638250551539796319801492816216875}{219670205947163758519}\cdot t^{13}-\frac{17130364713965763536033943177216932453461340625}{219670205947163758519}\cdot t^{11}+\frac{33016408607003353812065688818842780554127927500}{219670205947163758519}\cdot t^9-\frac{39209545288073892900395965401207404043847413750}{219670205947163758519}\cdot t^7+\frac{25621059462642942356182575706119494496350859375}{219670205947163758519}\cdot t^5-\frac{7530623484111515034703313166062955126966665625}{219670205947163758519}\cdot t^3+\frac{631971713300105923623685740773998690638356250}{219670205947163758519}\cdot t$

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.