Rule: Q[26, 28]

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.

• $P_1$:
  $\frac{61989816618513}{8388608}\cdot t^{26}-\frac{395033145117975}{8388608}\cdot t^{24}+\frac{556271163533475}{4194304}\cdot t^{22}-\frac{911337863661225}{4194304}\cdot t^{20}+\frac{1923935489951475}{8388608}\cdot t^{18}-\frac{1369126185872445}{8388608}\cdot t^{16}+\frac{166966608033225}{2097152}\cdot t^{14}-\frac{55655536011075}{2097152}\cdot t^{12}+\frac{49638721307175}{8388608}\cdot t^{10}-\frac{7091245901025}{8388608}\cdot t^8+\frac{300840735195}{4194304}\cdot t^6-\frac{13233463425}{4194304}\cdot t^4+\frac{456326325}{8388608}\cdot t^2-\frac{1300075}{8388608}$
• $P_2$:
  $\frac{61989816618513}{8388608}\cdot t^{54}-\frac{45158973663286539}{461373440}\cdot t^{52}+\frac{294839418254227692273}{482135244800}\cdot t^{50}-\frac{3749138791942800161490921}{1564528869376000}\cdot t^{48}+\frac{329406760054071326783096961321}{49865446389186560000}\cdot t^{46}-\frac{37353767696682963814902997019763}{2742599551405260800000}\cdot t^{44}+\frac{47918145192996646733723862016471697547}{2198234679444587610112000000}\cdot t^{42}-\frac{224755736524713573046603617982499963277147}{8100494793753305343262720000000}\cdot t^{40}+\frac{678025121951807412965879575042115222143500329499}{23752837868879004658888975974400000000}\cdot t^{38}-\frac{131314666771363694345959288795768795594698407817851733}{5472535080800378278384725619621888000000000}\cdot t^{36}+\frac{6928133922048441146671502220947600334536281948893630408063}{417472338638856856966578793892855726080000000000}\cdot t^{34}-\frac{217663850080629369213666839475503225456759141924349532511589}{22960978625137127133161833664107064934400000000000}\cdot t^{32}+\frac{1256814170674019562557620175420085456101991875516515487064365848419}{280654423936583462925577158416623305801158144000000000000}\cdot t^{30}-\frac{2131076154156573075410056540161987348930328124531418564831637926855103}{1219443472004455146411632753320228263706032135680000000000000}\cdot t^{28}+\frac{47942423233733743320268898947144871470926296832965446477084673200534208307}{85379334692391927076010467223715781883377839979635200000000000000}\cdot t^{26}-\frac{38805964180333961713637905874140212898559417318255665955789101196925147}{262705645207359775618493745303740867333470276860416000000000000}\cdot t^{24}+\frac{1441600484847486456579731688486163894615333997607088948364329772135277}{45687938296932134890172825270215803014516569888768000000000000}\cdot t^{22}-\frac{22476857384565900124953281205391848480707115168258173832778161564747}{4153448936084739535470256842746891183137869989888000000000000}\cdot t^{20}+\frac{160491872155868976609289158849723796641746563265970243889074444207}{218602575583407343972118781197204799112519473152000000000000}\cdot t^{18}-\frac{84439361586614074053611597306272882982137242059116524249190148799}{1093012877917036719860593905986023995562597365760000000000000}\cdot t^{16}+\frac{671437854703171083370605079519236978915467469835166124175720413}{109301287791703671986059390598602399556259736576000000000000}\cdot t^{14}-\frac{38953520875485771051170954886689241493440094976210032659092361}{109301287791703671986059390598602399556259736576000000000000}\cdot t^{12}+\frac{142740811305322861146094464576787910688024317373546387266121}{9936480708336697453278126418054763596023612416000000000000}\cdot t^{10}-\frac{3722363419823564779482325445295564884835243331918590083781}{9936480708336697453278126418054763596023612416000000000000}\cdot t^8+\frac{6175140851767999852688692236617951013744749944625341270923}{1093012877917036719860593905986023995562597365760000000000000}\cdot t^6-\frac{1261227701235426785816527830176951593256411319995746810077}{31260168308427250188012985711200286273090284660736000000000000}\cdot t^4+\frac{2697314573768881190689543633539763667641832351882029779}{31260168308427250188012985711200286273090284660736000000000000}\cdot t^2-\frac{10876423612091146276347573710708301501187414500039}{31260168308427250188012985711200286273090284660736000000000000}$

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.