Rule: Q[3, 50]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{53}-\frac{9056318089372798804507319}{1616144408082305758212}\cdot t^{51}+\frac{1955945242796634757321894975}{1077429605388203838808}\cdot t^{49}-\frac{194767443376951877331226496925}{538714802694101919404}\cdot t^{47}+\frac{53469571362395016467236194122575}{1077429605388203838808}\cdot t^{45}-\frac{21504083496258840081940537270662825}{4309718421552815355232}\cdot t^{43}+\frac{3286049618317892673249759021152285475}{8619436843105630710464}\cdot t^{41}-\frac{195378744983431466401237363579803496125}{8619436843105630710464}\cdot t^{39}+\frac{18366506534231411774757627170725100332875}{17238873686211261420928}\cdot t^{37}-\frac{5516272817054255256333790487801786943802875}{137910989489690091367424}\cdot t^{35}+\frac{332965552148572751326689738317602179249947625}{275821978979380182734848}\cdot t^{33}-\frac{2026277230094503889409113655665988212061745125}{68955494744845045683712}\cdot t^{31}+\frac{79621994457780886745750944155271579759172424375}{137910989489690091367424}\cdot t^{29}-\frac{5042254304193276553449367087125440495105631294375}{551643957958760365469696}\cdot t^{27}+\frac{128144993932235141393400856821563222351718352618125}{1103287915917520730939392}\cdot t^{25}-\frac{1298734692379102777681782959587671865761455206415625}{1103287915917520730939392}\cdot t^{23}+\frac{20809557480954443611354875612050438220340556395153125}{2206575831835041461878784}\cdot t^{21}-\frac{2083483884291533249707989278531939370964188937016671875}{35305213309360663390060544}\cdot t^{19}+\frac{20049691601772489389320983658675966048517514505278890625}{70610426618721326780121088}\cdot t^{17}-\frac{36337564962861265200955071148639435498829366300135765625}{35305213309360663390060544}\cdot t^{15}+\frac{193182855746022792189302163741047760124004328299200171875}{70610426618721326780121088}\cdot t^{13}-\frac{1452980251817892141118098657927200165959433306168536265625}{282441706474885307120484352}\cdot t^{11}+\frac{3677219652377608850646310248730828141779943291000392421875}{564883412949770614240968704}\cdot t^9-\frac{2912860702338642272737075189025469810256672160801304140625}{564883412949770614240968704}\cdot t^7+\frac{2579410162790565742608169127859331157817258592999839609375}{1129766825899541228481937408}\cdot t^5-\frac{4176107537655711194514235944514201970655886472477660953125}{9038134607196329827855499264}\cdot t^3+\frac{487518324789982753944853994360016241015864522633335984375}{18076269214392659655710998528}\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.