Rule: Q[1, 4, 10, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^5-10\cdot t^3+\frac{15}{2}\cdot t$
• $P_3$:
  $2\cdot t^{15}-\frac{1805}{21}\cdot t^{13}+\frac{169685}{126}\cdot t^{11}-\frac{2447225}{252}\cdot t^9+\frac{268675}{8}\cdot t^7-\frac{846835}{16}\cdot t^5+\frac{1039225}{32}\cdot t^3-\frac{327525}{64}\cdot t$
• $P_4$:
  $2\cdot t^{49}-\frac{4175800205808505672520320090786198999805978345308978443685245435150381643997343295853489}{4590629804181073661263159751716754087714196155258679218560831995805786188647872427496}\cdot t^{47}+\frac{1639633442027414667183921517477927533365639865733293557910836978694224563542005361199709720153}{8676290329902229219787371930744665225779830733438903723079972472072935896544478887967440}\cdot t^{45}-\frac{3224001978586333697225100349480918863501361774349694221876997003445050706332371000278738334502641}{135350129146474775828683002119616777522165359441646898080047570564337799986093870652292064}\cdot t^{43}+\frac{236744622419333190661335716380685164876887194671393693222072429147849178429133444756845441862551561}{116014396411264093567442573245385809304713165235697341211469346198003828559509031987678912}\cdot t^{41}-\frac{204913304471979855280122079027876331999195528039473245799213203871201803099814802953850243949393547175}{1624201549757697309944196025435401330265984313299762776960570846772053599833126447827504768}\cdot t^{39}+\frac{6316533025430263551483970362931845268601710122239858784069040298489318324671947729402795692387733947005}{1082801033171798206629464016956934220177322875533175184640380564514702399888750965218336512}\cdot t^{37}-\frac{9118187731350101871789057357350193072553957422696970314921971475049982440619167281652153329663607361551}{44195960537624416597120980283956498782747872470741844271035941408763363260765345519115776}\cdot t^{35}+\frac{3502705545374631251376036636993091822085826256436846332138207398476869859612758763804464314050421287821165}{618743447526741832359693723975390982958470214590385819794503179722687085650714837267620864}\cdot t^{33}-\frac{25067979424138137839153374150874514976438182329410632715812941909067995730721847733387997460237504089338635}{206247815842247277453231241325130327652823404863461939931501059907562361883571612422540288}\cdot t^{31}+\frac{845823351087858857131392077188279206277381522984991943535999708992932508774412080795127326786808437148569475}{412495631684494554906462482650260655305646809726923879863002119815124723767143224845080576}\cdot t^{29}-\frac{3205634250434898003043614006112402984493730884283728105036220656315531643217682298473803555745498140168579975}{117855894766998444258989280757217330087327659921978251389429177090035635362040921384308736}\cdot t^{27}+\frac{1330179635623195626049131204605440707400948836783403659056003712436407028024498971506436915444588391989345275}{4700804919481419429133475585757956185819336862984887519806291963705125057175421365755904}\cdot t^{25}-\frac{7195269663505307303147833907171441634427250020847203123040057995535839181800642264815269256739327243315488125}{3133869946320946286088983723838637457212891241989925013204194642470083371450280910503936}\cdot t^{23}+\frac{12896858368647880770186691960140958643016749497321164262734706386020166701602750824595437156586933435110866875}{895391413234556081739709635382467844917968926282835718058341326420023820414365974429696}\cdot t^{21}-\frac{41202187137980680290277682657151375631564035826849532330807614040520678758496402607458993471337691028977991875}{596927608823037387826473090254978563278645950855223812038894217613349213609577316286464}\cdot t^{19}+\frac{127221201665247331790886152292500751388320140206688740326828652008171602840322668239284286840539684012099044375}{511652236134032046708405505932838768524553672161620410319052186525727897379637699674112}\cdot t^{17}-\frac{9447119284826398906207668212197093454781066672534450982220901963909053216580797983806318632255270726235393354625}{14326262611752897307835354166119485518687502820525371488933461222720381126629855590875136}\cdot t^{15}+\frac{1709550630279463198340996190013364426054780341225152068435371517453887637624286058829132090403514989993405923125}{1364405963024085457889081349154236716065476459097654427517472497401941059679033865797632}\cdot t^{13}-\frac{31426373789790618575568913313928035074200404377195029518261909575910999869788663949923167981671865478150059650625}{19101683482337196410447138888159314024916670427367161985244614963627174835506474121166848}\cdot t^{11}+\frac{54245925137612520539265552783291583499632798397459586738346384885169279236529081016074534150271100401476833053125}{38203366964674392820894277776318628049833340854734323970489229927254349671012948242333696}\cdot t^9-\frac{2716809932920654938137836567477849613175758991348831697247691029853075398392163129876923655640419236839070940625}{3638415901397561221037550264411297909507937224260411806713259993071842825810756975460352}\cdot t^7+\frac{1521983973176400770096156310676939892621577306251042758179112904278014889618301667215480307033748794226530230625}{7276831802795122442075100528822595819015874448520823613426519986143685651621513950920704}\cdot t^5-\frac{331693360783493209857351330325205866213699516361766042363268026742383091397561171168445125333640941475310696875}{14553663605590244884150201057645191638031748897041647226853039972287371303243027901841408}\cdot t^3+\frac{4565967048866500492887700704482738760709333621071055677585247560936990098297633603659688510011099956590334375}{29107327211180489768300402115290383276063497794083294453706079944574742606486055803682816}\cdot t$

Warning: This rule has negative weights!

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.