Rule: Q[6, 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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{38}-\frac{13648276674734528586881411936}{700595787372387283311781}\cdot t^{36}+\frac{5546929808392009909442907600560}{2101787362117161849935343}\cdot t^{34}-\frac{1918956527942276315832719311117880}{9107745235841034683053153}\cdot t^{32}+\frac{14396247908198499158066916269702640}{1301106462263004954721879}\cdot t^{30}-\frac{3680523732514124464743563741532732920}{9107745235841034683053153}\cdot t^{28}+\frac{13772391545298501179996552794258949340}{1301106462263004954721879}\cdot t^{26}-\frac{20235436226387824196733857697339335250}{100085112481769611901683}\cdot t^{24}+\frac{567771204590218441979978666589798202125}{200170224963539223803366}\cdot t^{22}-\frac{1063768561239950286824372681751460223625}{36394586357007131600612}\cdot t^{20}+\frac{16003824658182293319730155073226952904875}{72789172714014263201224}\cdot t^{18}-\frac{173590228476213661729322651214910204349625}{145578345428028526402448}\cdot t^{16}+\frac{665803530047611859918874792800492954548125}{145578345428028526402448}\cdot t^{14}-\frac{3512986489956079566904748639984388065716875}{291156690856057052804896}\cdot t^{12}+\frac{82258807722551332686358643353739343575625}{3908143501423584601408}\cdot t^{10}-\frac{26707786577634422137723146749711103584664375}{1164626763424228211219584}\cdot t^8+\frac{133231971690197589573051168691884520603850625}{9317014107393825689756672}\cdot t^6-\frac{82029198926422262900053390708781415481809375}{18634028214787651379513344}\cdot t^4+\frac{18501201902498849290951060686243859083403125}{37268056429575302759026688}\cdot t^2-\frac{615962444143380278091548235801288166884375}{74536112859150605518053376}$

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.