Rule: Q[6, 49]

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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{55}-\frac{451261493390660924679193591805572348338819647869267555}{338071256417604147929271014526164762694207273539701}\cdot t^{53}+\frac{3063133597273350873226082394833122049069738012996792143895}{3718783820593645627221981159787812389636280008936711}\cdot t^{51}-\frac{561167442386030421079468183650662891420867949085426448364495}{1796715778489064741242080785066021716341124049261557}\cdot t^{49}+\frac{13047140420016694370019930160851080762184491753330640569271185430}{159907704285526761970545189870875932754360040384278573}\cdot t^{47}-\frac{2495554367940309582699404915516829440496889351529306451273467502090}{159907704285526761970545189870875932754360040384278573}\cdot t^{45}+\frac{32963953366630701802956231783154683537333703592299744209889832523450}{14537064025956978360958653624625084795850912762207143}\cdot t^{43}-\frac{86654435143940940742126025191672739739616586444420184338927812153050}{338071256417604147929271014526164762694207273539701}\cdot t^{41}+\frac{7741900548580754677214243575121618458662201522649186822619102678077575}{338071256417604147929271014526164762694207273539701}\cdot t^{39}-\frac{29076851698398510152833391154955370022790354418138404272706202684097675}{17793224021979165680487948132956040141800382817879}\cdot t^{37}+\frac{1668301435827925743750985974349213840302843609548357078255098256128977525}{17793224021979165680487948132956040141800382817879}\cdot t^{35}-\frac{4065295151665844901210824515166617824952311426482425323639299643775507125}{936485474841008720025681480681896849568441200941}\cdot t^{33}+\frac{2888993173584244114477385069812423705941347622788818288120736193181526059500}{17793224021979165680487948132956040141800382817879}\cdot t^{31}-\frac{4589320839063717477682809138185373476075200521983480940412821247056512569500}{936485474841008720025681480681896849568441200941}\cdot t^{29}+\frac{2117045027404276008504006094400706351808322664159217076335044989779645807705500}{17793224021979165680487948132956040141800382817879}\cdot t^{27}-\frac{41127947831478949850272526450707723835151989703077171972204254579153569392536500}{17793224021979165680487948132956040141800382817879}\cdot t^{25}+\frac{634536288777780564814503894722473883214695391693166437980564062530948389632790625}{17793224021979165680487948132956040141800382817879}\cdot t^{23}-\frac{7697018965317305490353286562133365191485313981658527762487679304473272882316784375}{17793224021979165680487948132956040141800382817879}\cdot t^{21}+\frac{72452797542102041637142978290235383589697801659554133765696861074679083335175590625}{17793224021979165680487948132956040141800382817879}\cdot t^{19}-\frac{27387898630214713066417356856280458413206309047161201551541975176619656685081440625}{936485474841008720025681480681896849568441200941}\cdot t^{17}+\frac{2789502315028622222295656431283191557650691245669799762756343749776688937832314631250}{17793224021979165680487948132956040141800382817879}\cdot t^{15}-\frac{10838417695210334963781225851152770123613709363372493658482122049393603257654631468750}{17793224021979165680487948132956040141800382817879}\cdot t^{13}+\frac{29315148941854219395233132710122584192932303525821954863332418436407126591281468406250}{17793224021979165680487948132956040141800382817879}\cdot t^{11}-\frac{52060413129361548752335677791175008971441909912014565426567272580406988850100965968750}{17793224021979165680487948132956040141800382817879}\cdot t^9+\frac{55419124056555958030372154729067193657452057866516426039550719731162827761120222296875}{17793224021979165680487948132956040141800382817879}\cdot t^7-\frac{30160231788089941534287376467415081947935734052196563660506576851267099079186735078125}{17793224021979165680487948132956040141800382817879}\cdot t^5+\frac{5917386825307713939043380126258033542434490762153289339140924397290006621137486171875}{17793224021979165680487948132956040141800382817879}\cdot t^3-\frac{50921732550984757027110272708475065757538784426139582027427669641357679954964765625}{17793224021979165680487948132956040141800382817879}\cdot t$

Warning: This rule has negative weights!

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.