Rule: Q[5, 44]

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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{49}-\frac{619354465161480516565332070000193}{6529306882322420126895308400706}\cdot t^{47}+\frac{23209853009644209559506970176200906123}{43289304629797645441315894696680780}\cdot t^{45}-\frac{3914663951462940102890493581237630592}{2071369952716123894772642273120747}\cdot t^{43}+\frac{211516229882048211354633220242404268516}{45418575304677936131722083013062233}\cdot t^{41}-\frac{1012514115880973126523992205119338677989}{118787043104542294498350063264931994}\cdot t^{39}+\frac{236982216009211690017574773472647235564857}{19718649155354020886726110501978711004}\cdot t^{37}-\frac{988021206206940278028792245116886164711117}{73944934332577578325222914382420166265}\cdot t^{35}+\frac{19616187311071527044193823710168310952906231}{1649407005818436335348501713753748649864}\cdot t^{33}-\frac{588066061048553172806134166170189643545003}{68725291909101513972854238073072860411}\cdot t^{31}+\frac{332802403166084562594339899429192341242239}{66508347008807916747923456199747929430}\cdot t^{29}-\frac{598557201477875302640824696988479395765676}{251126344740154030479228222547324078365}\cdot t^{27}+\frac{234676841610542709131101963269889851161867}{253988183426651512308051336194587030825}\cdot t^{25}-\frac{2950678358808590954959561355208520988061}{10159527337066060492322053447783481233}\cdot t^{23}+\frac{58276432628147824492722721865708774999161}{792443132291152718401120168927111536174}\cdot t^{21}-\frac{1708616913420168387253890209410018467306154}{115036328037599002954562611189252358001259}\cdot t^{19}+\frac{2172076721366148338272635482640857917566431}{920290624300792023636500889514018864010072}\cdot t^{17}-\frac{3586908946519787782053247055155509180988349}{12383322371106245612167622263313636184841410}\cdot t^{15}+\frac{2994634517995533459764582474570072358631}{111843248357484652295122803449751937987852}\cdot t^{13}-\frac{172129065971488106735949637853166224958836}{95542094909381264223108654846950593026122571}\cdot t^{11}+\frac{4298035260946225339379806635056306225}{51101138300613976229154210116037043872057}\cdot t^9-\frac{103277851286400360363352979074576935475}{40672538395158289187347459493079368918750974}\cdot t^7+\frac{25456128614369112445024279245457961631027}{573889516755683460433472653447349895443576243140}\cdot t^5-\frac{221418549431253480378541339366673373269}{602583992593467633455146286119717390215755055297}\cdot t^3+\frac{1467102465239690063736875506975806143}{1606890646915913689213723429652579707242013480792}\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.