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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^9-168\cdot t^7+432\cdot t^5-270\cdot t^3+45\cdot t$
• $P_3$:
  $16\cdot t^{45}-\frac{86706513550052870645640383681667356910534234943690212808}{12638783590828860632123548997686844617726134144104027}\cdot t^{43}+\frac{168668892312937094484233730697008461934828515011701727094553}{126387835908288606321235489976868446177261341441040270}\cdot t^{41}-\frac{39504247626660421809374555974773514280647038606974985352721877}{252775671816577212642470979953736892354522682882080540}\cdot t^{39}+\frac{1558201685052571638808814145407993705584528791596341302674697267}{126387835908288606321235489976868446177261341441040270}\cdot t^{37}-\frac{702447839400381310378862112486571562861096288894133893143265999367}{1011102687266308850569883919814947569418090731528322160}\cdot t^{35}+\frac{1063987169731455985129614828175210448425574877674409215588566771095}{36767370446047594566177597084179911615203299328302624}\cdot t^{33}-\frac{16723859046745210360884037519177044588967894409757271557403618714191}{18383685223023797283088798542089955807601649664151312}\cdot t^{31}+\frac{100416718876349873774826494909626249539410573633414444155657093331529}{4595921305755949320772199635522488951900412416037828}\cdot t^{29}-\frac{29666175209967479975357890408291305891741248312627076475184158310563653}{73534740892095189132355194168359823230406598656605248}\cdot t^{27}+\frac{1686990100445805656694561748568274097187038573591795879482012090288469959}{294138963568380756529420776673439292921626394626420992}\cdot t^{25}-\frac{36834139499552187992644126100677872386607002373232016367900762241507813125}{588277927136761513058841553346878585843252789252841984}\cdot t^{23}+\frac{153389568819856672815122746025743039609012282115401786891223438877882549975}{294138963568380756529420776673439292921626394626420992}\cdot t^{21}-\frac{7714151172102044229479176810052115812310076207867748781890393345095932707775}{2353111708547046052235366213387514343373011157011367936}\cdot t^{19}+\frac{72091049461644401722927997225807653747017881351264912273341742843197387508475}{4706223417094092104470732426775028686746022314022735872}\cdot t^{17}-\frac{245182318077374227500229673517899360328992725210820681133144314469641012844075}{4706223417094092104470732426775028686746022314022735872}\cdot t^{15}+\frac{590050878382222657190250100253772836315672809961835237265348655446525890474375}{4706223417094092104470732426775028686746022314022735872}\cdot t^{13}-\frac{3869653613294121835091421776148233501517444855833855649321511560976590850591875}{18824893668376368417882929707100114746984089256090943488}\cdot t^{11}+\frac{32838876128411029470368901193523982231275865703783988484632546202553667443987875}{150599149347010947343063437656800917975872714048727547904}\cdot t^9-\frac{41945074230774563199151579714039962970806053047193096721136498027546467432850875}{301198298694021894686126875313601835951745428097455095808}\cdot t^7+\frac{7259944929098067538350357608903378409932022046434444785613003709550752818907125}{150599149347010947343063437656800917975872714048727547904}\cdot t^5-\frac{9184715468338858129716731091085340093179946622292368655324726664713514937665625}{1204793194776087578744507501254407343806981712389820383232}\cdot t^3+\frac{902485577343800218303044285237121003782607943104032098185641202104703235161875}{2409586389552175157489015002508814687613963424779640766464}\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.