Rule: Q[20, 35]

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.

• $P_1$:
  $1048576\cdot t^{20}-99614720\cdot t^{18}+3810263040\cdot t^{16}-76205260800\cdot t^{14}+866834841600\cdot t^{12}-5721109954560\cdot t^{10}+21454162329600\cdot t^8-42908324659200\cdot t^6+40226554368000\cdot t^4-13408851456000\cdot t^2+670442572800$
• $P_2$:
  $1048576\cdot t^{55}-\frac{424004861224152240619612152388648960}{719676700547021253036700269}\cdot t^{53}+\frac{2533342344381053124811862770993250959360}{16552564112581488819844106187}\cdot t^{51}-\frac{1483283490473812683322475067728100519116800}{60692735079465459006095056019}\cdot t^{49}+\frac{163288939563059024513656838845797684527104000}{60692735079465459006095056019}\cdot t^{47}-\frac{13174346565636769911881446566572452885902295040}{60692735079465459006095056019}\cdot t^{45}+\frac{808480900877080537244927000451797133512225587200}{60692735079465459006095056019}\cdot t^{43}-\frac{38659503520725443420359497743970624954822058598400}{60692735079465459006095056019}\cdot t^{41}+\frac{63647170183696104579852343229216317552355507712000}{2638814568672411261134567653}\cdot t^{39}-\frac{4033908040187693996725770844524145873488668059008000}{5517521370860496273281368729}\cdot t^{37}+\frac{1084193211643649942703850315469435132556249562381363200}{60692735079465459006095056019}\cdot t^{35}-\frac{1948893430580340937153407562879524469130800540344864000}{5517521370860496273281368729}\cdot t^{33}+\frac{31230286126290154326017055389919521623868580757400448000}{5517521370860496273281368729}\cdot t^{31}-\frac{17620590387581114520423292817241142873732038827101920000}{239892233515673751012233423}\cdot t^{29}+\frac{4246916008998816079348876483355191260007611951230328960000}{5517521370860496273281368729}\cdot t^{27}-\frac{35761526946255420035344306058144204802628488026342809080000}{5517521370860496273281368729}\cdot t^{25}+\frac{240257681140217354845162297042393162796645110961152794150000}{5517521370860496273281368729}\cdot t^{23}-\frac{55456291971079822387245385406127838217338570428582558412500}{239892233515673751012233423}\cdot t^{21}+\frac{229740613105316570649636500935387566755220644570285638875000}{239892233515673751012233423}\cdot t^{19}-\frac{730764101697366605018505203633836194519293057643132147984375}{239892233515673751012233423}\cdot t^{17}+\frac{1747806276517156098042662907120883510998470372377928440443750}{239892233515673751012233423}\cdot t^{15}-\frac{6117473506340718840308388013001127194412665668651164946640625}{479784467031347502024466846}\cdot t^{13}+\frac{3776882054730346556982346888744350662902130976412692812812500}{239892233515673751012233423}\cdot t^{11}-\frac{25037541456114778088123192160974200278311805698116148137734375}{1919137868125390008097867384}\cdot t^9+\frac{25895722170111905470748617607703816783467729776453937816484375}{3838275736250780016195734768}\cdot t^7-\frac{29840586116328757156238987596946094053035661541468939677109375}{15353102945003120064782939072}\cdot t^5+\frac{1957513691382290227864264235757107246321303934253030904296875}{7676551472501560032391469536}\cdot t^3-\frac{590723060430682154443963092740687252745393152679878698828125}{61412411780012480259131756288}\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.