Rule: Q[1, 16, 32]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{17}-136\cdot t^{15}+7140\cdot t^{13}-185640\cdot t^{11}+2552550\cdot t^9-18378360\cdot t^7+64324260\cdot t^5-91891800\cdot t^3+34459425\cdot t$
• $P_3$:
  $t^{49}-\frac{167775971289269966314312}{182562970566544874259}\cdot t^{47}+\frac{776996009026283263559808428}{2008192676231993616849}\cdot t^{45}-\frac{66366742306105973435104456680}{669397558743997872283}\cdot t^{43}+\frac{1512838797767891068086758024270}{87312725053564939863}\cdot t^{41}-\frac{83686753345166276816944775523612760}{38155660848407878720131}\cdot t^{39}+\frac{2651448366883117020578698906128731260}{12718553616135959573377}\cdot t^{37}-\frac{580780419543037639125738220553989347320}{38155660848407878720131}\cdot t^{35}+\frac{33052981955269782541097841005583381586925}{38155660848407878720131}\cdot t^{33}-\frac{44829993136218500232845833332282862392400}{1156232146921450870307}\cdot t^{31}+\frac{1585466870322066287072078235785465250533000}{1156232146921450870307}\cdot t^{29}-\frac{44361405782309444768303889167503353176138000}{1156232146921450870307}\cdot t^{27}+\frac{980233618208415624226513729392465164787220500}{1156232146921450870307}\cdot t^{25}-\frac{740201309345771546084937412136256432056850000}{50270962909628298709}\cdot t^{23}+\frac{10026764711823956386679972980429353469477875000}{50270962909628298709}\cdot t^{21}-\frac{5514070895009658769712962702397306714504910000}{2645840153138331511}\cdot t^{19}+\frac{43779794487183597046856973991206990888701345625}{2645840153138331511}\cdot t^{17}-\frac{258911346189438302106124740171571572672597645000}{2645840153138331511}\cdot t^{15}+\frac{1110708722696514233587045914408297534814458262500}{2645840153138331511}\cdot t^{13}-\frac{3335137082083930055283601919890077949002790425000}{2645840153138331511}\cdot t^{11}+\frac{6670706651398248390455085920213088091373033268750}{2645840153138331511}\cdot t^9-\frac{8269557871989836163914406579157240478999723775000}{2645840153138331511}\cdot t^7+\frac{5676442368348896808047519366042881017581044912500}{2645840153138331511}\cdot t^5-\frac{1766986662355640234758288604389903025276203875000}{2645840153138331511}\cdot t^3+\frac{158205616476766585577348697879052420862924484375}{2645840153138331511}\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.