Rule: Q[10, 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.

• $P_1$:
  $1024\cdot t^{10}-23040\cdot t^8+161280\cdot t^6-403200\cdot t^4+302400\cdot t^2-30240$
• $P_2$:
  $1024\cdot t^{60}-\frac{1215016009095548025831063958431217220466357605738142901498460807040}{1555036687794148292920053245610087130846944934883434495670771}\cdot t^{58}+\frac{18532445545745995003927608469504949366234843131036477822408435334111040}{66866577575148376595562289561233746626418632199987683313843153}\cdot t^{56}-\frac{28446520386590174965927073231829716839318582948561396179552324539409163200}{468066043026038636168936026928636226384930425399913783196902071}\cdot t^{54}+\frac{177349666601422841017861438948274117097378996444670996213703500811966384762400}{19190707764067584082926377104074085281782147441396465111072984911}\cdot t^{52}-\frac{2840874651809428411353644758195604469154790685018211644055649840831478044642520}{2741529680581083440418053872010583611683163920199495015867569273}\cdot t^{50}+\frac{243865772397481510916507350916713403569783139332933817594571963882449283024163500}{2741529680581083440418053872010583611683163920199495015867569273}\cdot t^{48}-\frac{16424477500117034439362893165326317039145350328976592233487081311278298023913677000}{2741529680581083440418053872010583611683163920199495015867569273}\cdot t^{46}+\frac{882517332839913523265525128009377847695988517834665437622945637453660226538179945000}{2741529680581083440418053872010583611683163920199495015867569273}\cdot t^{44}-\frac{161806840260447656030313538886419870869025034425079452090135602086207837078037763125}{11592091672647287274494942376366104066313589514585602604091202}\cdot t^{42}+\frac{278347227111725076345589360732686897076634993163499849612007620598253322625627989125}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{40}-\frac{8022505071050841186752934233240525043231844333859878143026519027205289755014565624375}{565467886470599379243655725676395320307979976321248907516644}\cdot t^{38}+\frac{378963633366278168606792729676396804029606790710339744988421399727883563088238058488125}{1130935772941198758487311451352790640615959952642497815033288}\cdot t^{36}-\frac{29360840282070420475070114379777809346899341524712047615322268367381755806428189366121875}{4523743091764795033949245805411162562463839810569991260133152}\cdot t^{34}+\frac{931820708516374283770996874732518598346194617807415403178109133981549769266677454869221875}{9047486183529590067898491610822325124927679621139982520266304}\cdot t^{32}-\frac{3020581817029515096977537299870800670961133676547937620979987557911469166258715062842574375}{2261871545882397516974622902705581281231919905284995630066576}\cdot t^{30}+\frac{127470764937521247835001761339776314630236345009719362595319040793633515967255190163557940625}{9047486183529590067898491610822325124927679621139982520266304}\cdot t^{28}-\frac{8702112542181446307115650910398999491918983261784683452722468016115544211262068281082491409375}{72379889468236720543187932886578600999421436969119860162130432}\cdot t^{26}+\frac{119195852961911610261236922206512921804877238225972308271295762575622301848499354087652228984375}{144759778936473441086375865773157201998842873938239720324260864}\cdot t^{24}-\frac{648705870199984056527684484837810503148136610357443937072556122139140385945947711597096852109375}{144759778936473441086375865773157201998842873938239720324260864}\cdot t^{22}+\frac{5541682051001726042978710648722706228280734199605255402561774963005718083223226889670865477390625}{289519557872946882172751731546314403997685747876479440648521728}\cdot t^{20}-\frac{73158146107495777283165409886560894765897068012710116076579816701768799620776246176513184819765625}{1158078231491787528691006926185257615990742991505917762594086912}\cdot t^{18}+\frac{365824213267915985670125997764403343233518020381655162585091005731340775577037968031316943106015625}{2316156462983575057382013852370515231981485983011835525188173824}\cdot t^{16}-\frac{337759620152323044340686035432792911562880570895605146716783696288875996344319601976384709566015625}{1158078231491787528691006926185257615990742991505917762594086912}\cdot t^{14}+\frac{222743373741858991225774008490774132265841722593286689099615888285270872541106285937816199983984375}{579039115745893764345503463092628807995371495752958881297043456}\cdot t^{12}-\frac{6417382648111294718092783436413837505144315807783471194103484156121964730167335512325953303617484375}{18529251703868600459056110818964121855851887864094684201505390592}\cdot t^{10}+\frac{7401941780673681563614877313638509127866991507254489097356668557302084069848092434054322529857109375}{37058503407737200918112221637928243711703775728189368403010781184}\cdot t^8-\frac{2491486312349906606203601953419755331068570423456215044507572632218895056199136103649176482531015625}{37058503407737200918112221637928243711703775728189368403010781184}\cdot t^6+\frac{847335992218394425614318893353462619561250434339540355625401298438747375623858005051074110010546875}{74117006815474401836224443275856487423407551456378736806021562368}\cdot t^4-\frac{225265444131559660069100055029893479128732840061620884403503547992388035225307910268641281422265625}{296468027261897607344897773103425949693630205825514947224086249472}\cdot t^2+\frac{5484937826469426761090580883942370416771820459429497666030730388927646928323064709801822892265625}{592936054523795214689795546206851899387260411651029894448172498944}$

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.