Rule: Q[1, 2, 42]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^{45}-\frac{762527411580585593007}{800788896593667320}\cdot t^{43}+\frac{330621627713348403455121}{1601577793187334640}\cdot t^{41}-\frac{8663631528680372585580561}{320315558637466928}\cdot t^{39}+\frac{1535772869449538402062592667}{640631117274933856}\cdot t^{37}-\frac{390704370723420465296997339291}{2562524469099735424}\cdot t^{35}+\frac{36917652528360486778214899215909}{5125048938199470848}\cdot t^{33}-\frac{330852861051256758479359872977199}{1281262234549867712}\cdot t^{31}+\frac{18229453024076752829950312788309255}{2562524469099735424}\cdot t^{29}-\frac{3108711955918656830557715636305084515}{20500195752797883392}\cdot t^{27}+\frac{102773515632197187781378336592581435485}{41000391505595766784}\cdot t^{25}-\frac{1314971476522493465593375286602560061275}{41000391505595766784}\cdot t^{23}+\frac{25900578182441782978707719481374119881825}{82000783011191533568}\cdot t^{21}-\frac{777877942203416774175780477037583950626375}{328003132044766134272}\cdot t^{19}+\frac{8781680252601220464036986745916532717429625}{656006264089532268544}\cdot t^{17}-\frac{18274177354789032174786779469600124085958375}{328003132044766134272}\cdot t^{15}+\frac{6826317751510180805720393918312075278527375}{41000391505595766784}\cdot t^{13}-\frac{3616185682017306092521939048990765354684416375}{10496100225432516296704}\cdot t^{11}+\frac{9849018371448012774440664422186942602336295625}{20992200450865032593408}\cdot t^9-\frac{8193392045325085515324066921275675746129670625}{20992200450865032593408}\cdot t^7+\frac{7408941862531761611815879609450855109811466875}{41984400901730065186816}\cdot t^5-\frac{5918878169021127078610941858630714939225504375}{167937603606920260747264}\cdot t^3+\frac{652039258754883799125597180996577436696375625}{335875207213840521494528}\cdot t$

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.