Rule: Q[1, 54]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{55}-1485\cdot t^{53}+\frac{1023165}{2}\cdot t^{51}-\frac{434845125}{4}\cdot t^{49}+\frac{63922233375}{4}\cdot t^{47}-\frac{13819986855675}{8}\cdot t^{45}+\frac{2280297831186375}{16}\cdot t^{43}-\frac{294158420223042375}{32}\cdot t^{41}+\frac{60302476145723686875}{128}\cdot t^{39}-\frac{4964903869331250219375}{256}\cdot t^{37}+\frac{330662597697461264610375}{512}\cdot t^{35}-\frac{17885840511817222949379375}{1024}\cdot t^{33}+\frac{196744245629989452443173125}{512}\cdot t^{31}-\frac{7037390324457315029698115625}{1024}\cdot t^{29}+\frac{204084319409262135861245353125}{2048}\cdot t^{27}-\frac{4775573074176733979153141263125}{4096}\cdot t^{25}+\frac{358167980563255048436485594734375}{32768}\cdot t^{23}-\frac{5330382298970795720848873851046875}{65536}\cdot t^{21}+\frac{62187793487992616743236861595546875}{131072}\cdot t^{19}-\frac{559690141391933550689131754359921875}{262144}\cdot t^{17}+\frac{1902946480732574072343047964823734375}{262144}\cdot t^{15}-\frac{9514732403662870361715239824118671875}{524288}\cdot t^{13}+\frac{33734051249350176736990395740057109375}{1048576}\cdot t^{11}-\frac{80668383422359118284107468074049609375}{2097152}\cdot t^9+\frac{242005150267077354852322404222148828125}{8388608}\cdot t^7-\frac{203284326224344978075950819546605015625}{16777216}\cdot t^5+\frac{78186279317055760798442622902540390625}{33554432}\cdot t^3-\frac{8687364368561751199826958100282265625}{67108864}\cdot t$

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.