Rule: Q[6, 40]

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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{46}-\frac{6721756266524733727818046567124943297715155}{40250642675729374450411223121721717684048}\cdot t^{44}+\frac{51286816688587141311289038680683743634021526985}{56793656815454147349530235824749343652191728}\cdot t^{42}-\frac{8094815104903033523798997549655615452467031144895}{2669301870326344925427921083763219151653011216}\cdot t^{40}+\frac{1494228367366474760148235010740672822930155267418935}{210874847755781249108805765617294312980587886064}\cdot t^{38}-\frac{18056252170299989358601909218658589880457776929914769}{1476123934290468743761640359321060190864115202448}\cdot t^{36}+\frac{3409492270244978290291588328988666176465455956135295}{210874847755781249108805765617294312980587886064}\cdot t^{34}-\frac{15153783796274988101296600985801658297241522497618255}{905521405068943010878989464121322638093112687216}\cdot t^{32}+\frac{442230185624916297635174960886431204201898951353307075}{32146009879947476886204125976306953652305500396168}\cdot t^{30}-\frac{873467952855633124668723021576824890857050681164825769}{96438029639842430658612377928920860956916501188504}\cdot t^{28}+\frac{51634753976572707652244975371372509332748510595527116013}{10768913309782404756878382202062829473522342632716280}\cdot t^{26}-\frac{4396795348537224195696435407586323279496759146490531345}{2153782661956480951375676440412565894704468526543256}\cdot t^{24}+\frac{10504951348242592871876736448364110318627366012385715405}{15076478633695366659629735082887961262931279685802792}\cdot t^{22}-\frac{24881222999524029604039916941989757427214181905455868015}{131380742379345338033916262865166519576972580119138616}\cdot t^{20}+\frac{314400321029941285443103883509163542087673408250194061165}{7751463800381374944001059509044824655041382227029178344}\cdot t^{18}-\frac{52264991928637159064681645835388938453288028647258039141}{7751463800381374944001059509044824655041382227029178344}\cdot t^{16}+\frac{167210550869968260126709781369234920986987820986728985}{196239589883072783392431886304932269747883094355169072}\cdot t^{14}-\frac{1233195155635837174508968642783033388105441084652636855}{15502927600762749888002119018089649310082764454058356688}\cdot t^{12}+\frac{81723415312275295634256409834130713715567518547638855}{15502927600762749888002119018089649310082764454058356688}\cdot t^{10}-\frac{3023867799403758292688973666175464315504049523913094815}{12913938691435370656705765142068677875298942790230611121104}\cdot t^8+\frac{29360718445562667180472473800038819034118825690304197261}{4595517325766501186550580138413296655338523784352064614667152}\cdot t^6-\frac{425397390473291229143328672710003786591990966604228765}{4595517325766501186550580138413296655338523784352064614667152}\cdot t^4+\frac{2453350751214196457615749891944771311807170717321605}{4595517325766501186550580138413296655338523784352064614667152}\cdot t^2-\frac{2355783063269312651092917538073872978764968061405}{4595517325766501186550580138413296655338523784352064614667152}$

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.