Rule: Q[4, 5, 36]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^9-21\cdot t^7+108\cdot t^5-135\cdot t^3+45\cdot t$
• $P_3$:
  $t^{45}-\frac{10838314193756608830705047960208419613816779367961276601}{12638783590828860632123548997686844617726134144104027}\cdot t^{43}+\frac{168668892312937094484233730697008461934828515011701727094553}{505551343633154425284941959907473784709045365764161080}\cdot t^{41}-\frac{39504247626660421809374555974773514280647038606974985352721877}{505551343633154425284941959907473784709045365764161080}\cdot t^{39}+\frac{1558201685052571638808814145407993705584528791596341302674697267}{126387835908288606321235489976868446177261341441040270}\cdot t^{37}-\frac{702447839400381310378862112486571562861096288894133893143265999367}{505551343633154425284941959907473784709045365764161080}\cdot t^{35}+\frac{1063987169731455985129614828175210448425574877674409215588566771095}{9191842611511898641544399271044977903800824832075656}\cdot t^{33}-\frac{16723859046745210360884037519177044588967894409757271557403618714191}{2297960652877974660386099817761244475950206208018914}\cdot t^{31}+\frac{401666875505399495099305979638504998157642294533657776622628373326116}{1148980326438987330193049908880622237975103104009457}\cdot t^{29}-\frac{29666175209967479975357890408291305891741248312627076475184158310563653}{2297960652877974660386099817761244475950206208018914}\cdot t^{27}+\frac{1686990100445805656694561748568274097187038573591795879482012090288469959}{4595921305755949320772199635522488951900412416037828}\cdot t^{25}-\frac{36834139499552187992644126100677872386607002373232016367900762241507813125}{4595921305755949320772199635522488951900412416037828}\cdot t^{23}+\frac{153389568819856672815122746025743039609012282115401786891223438877882549975}{1148980326438987330193049908880622237975103104009457}\cdot t^{21}-\frac{7714151172102044229479176810052115812310076207867748781890393345095932707775}{4595921305755949320772199635522488951900412416037828}\cdot t^{19}+\frac{72091049461644401722927997225807653747017881351264912273341742843197387508475}{4595921305755949320772199635522488951900412416037828}\cdot t^{17}-\frac{245182318077374227500229673517899360328992725210820681133144314469641012844075}{2297960652877974660386099817761244475950206208018914}\cdot t^{15}+\frac{590050878382222657190250100253772836315672809961835237265348655446525890474375}{1148980326438987330193049908880622237975103104009457}\cdot t^{13}-\frac{3869653613294121835091421776148233501517444855833855649321511560976590850591875}{2297960652877974660386099817761244475950206208018914}\cdot t^{11}+\frac{32838876128411029470368901193523982231275865703783988484632546202553667443987875}{9191842611511898641544399271044977903800824832075656}\cdot t^9-\frac{41945074230774563199151579714039962970806053047193096721136498027546467432850875}{9191842611511898641544399271044977903800824832075656}\cdot t^7+\frac{7259944929098067538350357608903378409932022046434444785613003709550752818907125}{2297960652877974660386099817761244475950206208018914}\cdot t^5-\frac{9184715468338858129716731091085340093179946622292368655324726664713514937665625}{9191842611511898641544399271044977903800824832075656}\cdot t^3+\frac{902485577343800218303044285237121003782607943104032098185641202104703235161875}{9191842611511898641544399271044977903800824832075656}\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.