Rule: Q[1, 2, 48]

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^{51}-\frac{2344976159974179967385637}{1869618530014239455359}\cdot t^{49}+\frac{678019476088980160981433406}{1869618530014239455359}\cdot t^{47}-\frac{5221825028973486057153334683}{81287762174532150233}\cdot t^{45}+\frac{2540586260148730622376293304405}{325151048698128600932}\cdot t^{43}-\frac{450844265050578767750980480894935}{650302097396257201864}\cdot t^{41}+\frac{30262007853750280315221496719312345}{650302097396257201864}\cdot t^{39}-\frac{3145685182631694217441051641129408795}{1300604194792514403728}\cdot t^{37}+\frac{1028277585356073646155476110137832105215}{10404833558340115229824}\cdot t^{35}-\frac{66708888101444100572481533794316088178725}{20809667116680230459648}\cdot t^{33}+\frac{431885536528695326617583503361498288717025}{5202416779170057614912}\cdot t^{31}-\frac{17902179217123155372491530082857939444211475}{10404833558340115229824}\cdot t^{29}+\frac{1187372641304418682953950865158634139224390075}{41619334233360460919296}\cdot t^{27}-\frac{31410841200754604013971321257184788153542699225}{83238668466720921838592}\cdot t^{25}+\frac{329599511638820395587706812375926298728859283125}{83238668466720921838592}\cdot t^{23}-\frac{5442102461336983142919540081718567570325208219375}{166477336933441843677184}\cdot t^{21}+\frac{559120781768415539427274652443133714719483935654375}{2663637390935069498834944}\cdot t^{19}-\frac{5500373980676034244294564056958520571110258377348125}{5327274781870138997669888}\cdot t^{17}+\frac{10155895740065123007105690263201537133413003536993125}{2663637390935069498834944}\cdot t^{15}-\frac{54833189434013809107391565823274537793676991119009375}{5327274781870138997669888}\cdot t^{13}+\frac{417625196690966172453226304445079688935821593204053125}{21309099127480555990679552}\cdot t^{11}-\frac{1067396827086397850608757702417809003307283145828134375}{42618198254961111981359104}\cdot t^9+\frac{851738217647749489895079613911763451198793681762028125}{42618198254961111981359104}\cdot t^7-\frac{757964649145972610934670260356793726595913701235334375}{85236396509922223962718208}\cdot t^5+\frac{1230425455805217450376678266975759344075171227523390625}{681891172079377791701745664}\cdot t^3-\frac{143709179564057665903468732002823497258858354358546875}{1363782344158755583403491328}\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.