Rule: Q[22, 24]

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.

• $P_1$:
  $\frac{263012370465}{524288}\cdot t^{22}-\frac{1412926920405}{524288}\cdot t^{20}+\frac{3273855059475}{524288}\cdot t^{18}-\frac{4281195077775}{524288}\cdot t^{16}+\frac{1735619626125}{262144}\cdot t^{14}-\frac{902522205585}{262144}\cdot t^{12}+\frac{300840735195}{262144}\cdot t^{10}-\frac{62386327575}{262144}\cdot t^8+\frac{15058768725}{524288}\cdot t^6-\frac{929553625}{524288}\cdot t^4+\frac{22309287}{524288}\cdot t^2-\frac{88179}{524288}$
• $P_2$:
  $\frac{263012370465}{524288}\cdot t^{46}-\frac{138998979507375}{24641536}\cdot t^{44}+\frac{1679770618028676225}{56749457408}\cdot t^{42}-\frac{4365110740150210577175}{45342816468992}\cdot t^{40}+\frac{1203080522311943812262954475}{5534498835388694528}\cdot t^{38}-\frac{1035105923615686180703614119015}{2861335897895955070976}\cdot t^{36}+\frac{18461282591265728300651914190486775}{40159605151546532126261248}\cdot t^{34}-\frac{2691505827100655224647056414603431064775}{5902217009517642280064489357312}\cdot t^{32}+\frac{7866502598762643999448641208597021524812289075}{21972770531923773921402940947156434944}\cdot t^{30}-\frac{3936089954196539890162810313907925572906106676525}{17556243655007095363200949816777991520256}\cdot t^{28}+\frac{49974248656540169903280925657867240969316634279108177}{444752320512294746835969661708436859182645248}\cdot t^{26}-\frac{63084721079496823527459680137362496828225382688301316325}{1400525057293216157786468464719867669566149885952}\cdot t^{24}+\frac{794104189546236332108427281105541380083069521789556238901750375}{55215780213713312734052513050283271905102624524201099264}\cdot t^{22}-\frac{2601766946606519211205410137914776424042800633646590842324595}{717088054723549516026656013640042492274060058755858432}\cdot t^{20}+\frac{26963537266585705435540465505513563136726142190058155656825}{37741476564397342948771369138949604856529476776624128}\cdot t^{18}-\frac{239557657210350097114250528178790273158769761890923516065}{2220086856729255467574786419938212050384086869213184}\cdot t^{16}+\frac{54183507781286793586326076587875288065397231352071460075}{4440173713458510935149572839876424100768173738426368}\cdot t^{14}-\frac{4437216052843227681116329390069716744948150504549628875}{4440173713458510935149572839876424100768173738426368}\cdot t^{12}+\frac{250953408671510546841899249856833960480510864609001915}{4440173713458510935149572839876424100768173738426368}\cdot t^{10}-\frac{63977092191783767909410134890606336660372349528118725}{31081215994209576546047009879134968705377216168984576}\cdot t^8+\frac{191842055985012128734882058673429746097272007548685}{4440173713458510935149572839876424100768173738426368}\cdot t^6-\frac{20928688273828058390685516547643901537803054774175}{48841910848043620286645301238640665108449911122690048}\cdot t^4+\frac{62109409948412967599903303660800968097867944375}{48841910848043620286645301238640665108449911122690048}\cdot t^2-\frac{444375538973829130373661850923600104053599}{48841910848043620286645301238640665108449911122690048}$

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.