Rule: Q[1, 52]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{53}-1378\cdot t^{51}+\frac{878475}{2}\cdot t^{49}-86090550\cdot t^{47}+\frac{46531942275}{4}\cdot t^{45}-\frac{4606662285225}{4}\cdot t^{43}+\frac{1386605347852725}{16}\cdot t^{41}-\frac{40607728044258375}{8}\cdot t^{39}+\frac{30090326480795455875}{128}\cdot t^{37}-\frac{1113342079789431867375}{128}\cdot t^{35}+\frac{132487707494942392217625}{512}\cdot t^{33}-\frac{397463122484827176652875}{64}\cdot t^{31}+\frac{61606783985148212381195625}{512}\cdot t^{29}-\frac{962013626845006701029439375}{512}\cdot t^{27}+\frac{48238111860371050294476174375}{2048}\cdot t^{25}-\frac{241190559301855251472380871875}{1024}\cdot t^{23}+\frac{61021211503369378622512360584375}{32768}\cdot t^{21}-\frac{376895718109046162080223403609375}{32768}\cdot t^{19}+\frac{7161018644071877079524244668578125}{131072}\cdot t^{17}-\frac{6407227207853784755363797861359375}{32768}\cdot t^{15}+\frac{134551771364929479862639755088546875}{262144}\cdot t^{13}-\frac{249881861106297605459188116593015625}{262144}\cdot t^{11}+\frac{1249409305531488027295940582965078125}{1048576}\cdot t^9-\frac{488899293468843141115802836812421875}{524288}\cdot t^7+\frac{3422295054281901987810619857686953125}{8388608}\cdot t^5-\frac{684459010856380397562123971537390625}{8388608}\cdot t^3+\frac{157952079428395476360490147277859375}{33554432}\cdot t$

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.