Rule: Q[1, 66]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{67}-2211\cdot t^{65}+1149720\cdot t^{63}-374233860\cdot t^{61}+85605995475\cdot t^{59}-\frac{29294371651545}{2}\cdot t^{57}+\frac{3896151429655485}{2}\cdot t^{55}-\frac{826540696148342175}{4}\cdot t^{53}+\frac{569486539646207758575}{32}\cdot t^{51}-\frac{80677259783212765798125}{64}\cdot t^{49}+\frac{2371911437626455314464875}{32}\cdot t^{47}-\frac{233094205824927108630593625}{64}\cdot t^{45}+\frac{38460543961112972924047948125}{256}\cdot t^{43}-\frac{2671528553606539580801176704375}{512}\cdot t^{41}+\frac{78237621927048659152034460628125}{512}\cdot t^{39}-\frac{3864938523196203762110502355029375}{1024}\cdot t^{37}+\frac{1287024528224335852782797284224781875}{16384}\cdot t^{35}-\frac{45045858487851754847397904947867365625}{32768}\cdot t^{33}+\frac{165168147788789767773792318142180340625}{8192}\cdot t^{31}-\frac{4042273090620381158674390944005992546875}{16384}\cdot t^{29}+\frac{164116287479187475042180272326643297403125}{65536}\cdot t^{27}-\frac{2743086519294990654276441694602466542309375}{131072}\cdot t^{25}+\frac{18702862631556754460975738826834999152109375}{131072}\cdot t^{23}-\frac{205731488947124299070733127095184990673203125}{262144}\cdot t^{21}+\frac{7200602113149350467475659448331474673562109375}{2097152}\cdot t^{19}-\frac{49252118453941557197533510626587286767164828125}{4194304}\cdot t^{17}+\frac{64406616439769728642928436973229528849369390625}{2097152}\cdot t^{15}-\frac{250470175043548944722499477118114834414214296875}{4194304}\cdot t^{13}+\frac{1395476689528344120596782801086639791736336796875}{16777216}\cdot t^{11}-\frac{2646593721519273332166312208957420294672362890625}{33554432}\cdot t^9+\frac{1587956232911563999299787325374452176803417734375}{33554432}\cdot t^7-\frac{1075712286811059483396630123640757926221670078125}{67108864}\cdot t^5+\frac{5378561434055297416983150618203789631108350390625}{2147483648}\cdot t^3-\frac{488960130368663401543922783473071784646213671875}{4294967296}\cdot t$

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.