Rule: Q[8, 35]

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.

• $P_1$:
  $\frac{6435}{128}\cdot t^8-\frac{3003}{32}\cdot t^6+\frac{3465}{64}\cdot t^4-\frac{315}{32}\cdot t^2+\frac{35}{128}$
• $P_2$:
  $\frac{6435}{128}\cdot t^{43}-\frac{4551063707455968531535762993585220095987269}{8751425059818267299241136484562151497344}\cdot t^{41}+\frac{182174829642923145261524541548448432304471106873}{72965006436234803607422975440036938109105600}\cdot t^{39}-\frac{1376689504394098359254053280901204504296045504526813}{186425591444579923216965702249294376868764808000}\cdot t^{37}+\frac{375923686475138604070977095984529740694108436543498819}{24959723471694329148420036592576955714486625436800}\cdot t^{35}-\frac{38691004119249956405488216397983129865592827047937675077}{1722220919546908711240982524887809944299577155139200}\cdot t^{33}+\frac{11086853690762471190179390782509586182169915495215779431}{437078793975920013837673595331376008591180565887600}\cdot t^{31}-\frac{312097426617274144068576855627781229967614129387554927}{14099315934707097220570115978431484148102598899600}\cdot t^{29}+\frac{1322575022233661199776759825131226402489678270235855259}{87512995456802672403538650900609211953740269032000}\cdot t^{27}-\frac{64225960694316017903705147216481455986552693378568927}{7908581811651797061653122525832832487671342831040}\cdot t^{25}+\frac{119461638486196804923174553004931520065758859934016809}{34747279661831831770880208544350636355407070098080}\cdot t^{23}-\frac{34770839482775206648804103627397592614250062426629659}{30430847405703653911143536675487203267778862632480}\cdot t^{21}+\frac{5999590371399934423133774857420430425753338309122413}{20287231603802435940762357783658135511852575088320}\cdot t^{19}-\frac{316307184733766059444836389828888960229511981435460183}{5376116375007645524302024812669405910640932398404800}\cdot t^{17}+\frac{7118885667442210488534199456028128396265505488209709}{806417456251146828645303721900410886596139859760720}\cdot t^{15}-\frac{410759443533015565735231448865514193760323434410613}{422409143750600719766587663852596178693216117017520}\cdot t^{13}+\frac{589267456296748046928073029554726503936796825006459347}{7782466064461067660979611118820231996243813739930788480}\cdot t^{11}-\frac{175906930102702738447706378576109853124055823840353877}{44572305641913387512883227316879510523941842328694515840}\cdot t^9+\frac{224417583784585967960881321147781640560074348864373}{1768742287377515377495366163368234544600866759075179200}\cdot t^7-\frac{779704580947747686025891339303553559201924298159}{353748457475503075499073232673646908920173351815035840}\cdot t^5+\frac{1496430139451585323496515853932117636101192541}{92282206297957324043236495480081802327001743951748480}\cdot t^3-\frac{327545684950348067168617942764749552687071}{11598310081164035262264696153234324882628634485738880}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.