Rule: Q[1, 2, 6, 10, 18]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^9-\frac{117}{4}\cdot t^7+\frac{945}{8}\cdot t^5-\frac{2205}{16}\cdot t^3+\frac{945}{32}\cdot t$
• $P_4$:
  $2\cdot t^{19}-\frac{23713751}{205892}\cdot t^{17}+\frac{2134183615}{823568}\cdot t^{15}-\frac{48885080515}{1647136}\cdot t^{13}+\frac{623352876985}{3294272}\cdot t^{11}-\frac{4536269518165}{6588544}\cdot t^9+\frac{18427952550645}{13177088}\cdot t^7-\frac{38805894891225}{26354176}\cdot t^5+\frac{36681698574675}{52708352}\cdot t^3-\frac{11110847880825}{105416704}\cdot t$
• $P_5$:
  $2\cdot t^{37}-\frac{2866523542400994253836929184413188376368628899936493274794597330527311181985025656260490723674554611}{6122139611368566484345411551199224025655026036309221039722779169101440508986888728096891216039042}\cdot t^{35}+\frac{4748704722524508474016000413552696348086879253107726532862701417559097003772550510490437472874946610455}{97954233781897063749526584819187584410480416580947536635564466705623048143790219649550259456624672}\cdot t^{33}-\frac{1152158483373137211013565928808746431672248686614330121197187621375730417482191212876507163640384742033805}{391816935127588254998106339276750337641921666323790146542257866822492192575160878598201037826498688}\cdot t^{31}+\frac{91452121262687374459126099790959544035485169237696837103964497851917947652318042599458453403240724830956145}{783633870255176509996212678553500675283843332647580293084515733644984385150321757196402075652997376}\cdot t^{29}-\frac{5025020280819588216765994152512476889386333923391487982881788219269453584203219264220204465575559056972955495}{1567267740510353019992425357107001350567686665295160586169031467289968770300643514392804151305994752}\cdot t^{27}+\frac{197267806720891019128486393414880517673404163909547101819765336209181249098624497240090337844685332105456710135}{3134535481020706039984850714214002701135373330590321172338062934579937540601287028785608302611989504}\cdot t^{25}-\frac{5630775206349072298779825078261263813427657737986435996216175216471291171430342617313393367020426201439785947625}{6269070962041412079969701428428005402270746661180642344676125869159875081202574057571216605223979008}\cdot t^{23}+\frac{117827251880676519795356833890568978832753157614746877795854859727103670235262802817099891916721740998086050477125}{12538141924082824159939402856856010804541493322361284689352251738319750162405148115142433210447958016}\cdot t^{21}-\frac{1809399282816597579539677043320902614319267046148827542771804696941324276669521665932302879325879120449348452484875}{25076283848165648319878805713712021609082986644722569378704503476639500324810296230284866420895916032}\cdot t^{19}+\frac{20279540837768995742832549168121618543323743387871741122190758369918334792304926786272818500357553664363327797593375}{50152567696331296639757611427424043218165973289445138757409006953279000649620592460569732841791832064}\cdot t^{17}-\frac{163854704317572226565660429144981371079016061146111795493328319749736339739696351180546237273758636292945461890796375}{100305135392662593279515222854848086436331946578890277514818013906558001299241184921139465683583664128}\cdot t^{15}+\frac{934826895831672213617875418150155073511034356371058996826781316338428261150599585120616199740395717842743942118701875}{200610270785325186559030445709696172872663893157780555029636027813116002598482369842278931367167328256}\cdot t^{13}-\frac{3646072911592657438924826296658843377792232993334241535003041169410227240174245851275618697382292248549432865784633125}{401220541570650373118060891419392345745327786315561110059272055626232005196964739684557862734334656512}\cdot t^{11}+\frac{9246498376070694984101280222661815837983637074083024186759545471071402912169736142198118187821525303445848638271463125}{802441083141300746236121782838784691490655572631122220118544111252464010393929479369115725468669313024}\cdot t^9-\frac{14075162454890542561214993396182670539436769553388364727278752223859203913472759584421765867586855866074412261237221875}{1604882166282601492472243565677569382981311145262244440237088222504928020787858958738231450937338626048}\cdot t^7+\frac{11223670470821662156664682589875885264407039996102127715344231731440924098308902639468784234646698023479273018219384375}{3209764332565202984944487131355138765962622290524488880474176445009856041575717917476462901874677252096}\cdot t^5-\frac{3612597752089611750681961089938521768889926518371641578303796313820979622783857032689145772204954865076723960404165625}{6419528665130405969888974262710277531925244581048977760948352890019712083151435834952925803749354504192}\cdot t^3+\frac{247911845247377686610893496015462280834169800553184099839536121747826533047532604715178862440935597412091623909134375}{12839057330260811939777948525420555063850489162097955521896705780039424166302871669905851607498709008384}\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.