Rule: Q[1, 18, 34]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{19}-171\cdot t^{17}+5814\cdot t^{15}-101745\cdot t^{13}+\frac{3968055}{4}\cdot t^{11}-\frac{43648605}{8}\cdot t^9+\frac{130945815}{8}\cdot t^7-\frac{392837445}{16}\cdot t^5+\frac{1964187225}{128}\cdot t^3-\frac{654729075}{256}\cdot t$
• $P_3$:
  $2\cdot t^{53}-\frac{3061558570264471841290086093}{2901478992069837568667224}\cdot t^{51}+\frac{34245045036362413294206051748257}{133468033635212528158692304}\cdot t^{49}-\frac{2550793581889149410320086405680715}{66734016817606264079346152}\cdot t^{47}+\frac{5742742771462797905442810989924313423}{1468148369987337809745615344}\cdot t^{45}-\frac{1716171089839142163170187022457340205845}{5872593479949351238982461376}\cdot t^{43}+\frac{194233306930768866606081325276853440957455}{11745186959898702477964922752}\cdot t^{41}-\frac{8525672266160762432011871199700439140326105}{11745186959898702477964922752}\cdot t^{39}+\frac{589752753844179602406613796809413977793367125}{23490373919797404955929845504}\cdot t^{37}-\frac{129914727437406066531179924655820607341149752895}{187922991358379239647438764032}\cdot t^{35}+\frac{5732345342914398176316605189421649572473135617725}{375845982716758479294877528064}\cdot t^{33}-\frac{2310319303532782456262836129397530189105533099075}{8541954152653601802156307456}\cdot t^{31}+\frac{65902304717862937085229252712915409284693221334125}{17083908305307203604312614912}\cdot t^{29}-\frac{3018472192386422892444019090328390785862352258428625}{68335633221228814417250459648}\cdot t^{27}+\frac{55270097716911525783999693288999130924991399370667875}{136671266442457628834500919296}\cdot t^{25}-\frac{17476889799790052040182048485677058651436833249145625}{5942228975759027340630474752}\cdot t^{23}+\frac{25013795630516928221690370245626900283615742025479375}{1485557243939756835157618688}\cdot t^{21}-\frac{14254894398666081509189195140070506702821007612895461875}{190151327224288874900175192064}\cdot t^{19}+\frac{97158373279936068445288693612391638306610847319790165625}{380302654448577749800350384128}\cdot t^{17}-\frac{124134321167117758996018943408813616751411600446773375625}{190151327224288874900175192064}\cdot t^{15}+\frac{462992392014303719803304337214155990289596110198204859375}{380302654448577749800350384128}\cdot t^{13}-\frac{2431020997524255459436667022300999137919186456329329115625}{1521210617794310999201401536512}\cdot t^{11}+\frac{4273425772336798009962415905194918823327415652895433396875}{3042421235588621998402803073024}\cdot t^9-\frac{2338896500065506578317923636764936318046033072351344390625}{3042421235588621998402803073024}\cdot t^7+\frac{1422303688780182091304639767531085538933057287919757190625}{6084842471177243996805606146048}\cdot t^5-\frac{1566264147545049139003701534683433249400076724271151203125}{48678739769417951974444849168384}\cdot t^3+\frac{121511881694425137006077550374778177431334247812912609375}{97357479538835903948889698336768}\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.