Rule: Q[1, 2, 10, 14, 28]

Type

This rule is of Legendre type.

Polynomials

One starts from the polynomial P1 and extends one by one with Pi 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.

Warning: This rule has negative weights!

Node locations in the complex plane

Plot of the node locations in the complex plane.

Magnitude of the Weights

Logarithmic magnitude of the weights
         plotted against the (real part) of the nodes.

Quadrature Rule Data

Nodes

Node (ball center) Error (ball radius)
-0.99696345573553342034 + 2.8183518427636856359e-852j 2.33e-236, 2.33e-236j
-0.98189373966174310941 + 3.4552489692592064667e-852j 1.78e-236, 1.78e-236j
-0.93054609618299054922 + 9.1916714323523675645e-853j 2.58e-237, 2.58e-237j
0.99953206505353089654 + 6.6711796252557607848e-850j 9.85e-237, 9.85e-237j
0.95151371618655174505 - 1.0945607384168647863e-860j 5.44e-237, 5.44e-237j
0.93054609618299054922 + 7.6368031343828370213e-872j 2.81e-237, 2.81e-237j
-0.99125588906108358532 - 4.7937211923183460467e-884j 2.29e-236, 2.29e-236j
-0.90591989788431806766 - 4.1483664088695667918e-886j 1.22e-237, 1.22e-237j
0.99125588906108358532 + 5.9113921795893401963e-883j 2.47e-236, 2.47e-236j
0.99696345573553342034 + 3.0473951289850996016e-896j 2.39e-236, 2.39e-236j
0.90591989788431806766 + 5.7480996814643038623e-907j 1.14e-237, 1.14e-237j
0.64533232741799124195 + 9.7046574240224458315e-920j 3.75e-242, 3.75e-242j
-0.87783567338819181439 + 1.0211361317079289922e-915j 3.7e-238, 3.7e-238j
-0.84648809715906767396 - 7.5422864863392931305e-916j 1.16e-238, 1.16e-238j
-0.99953206505353089654 + 2.3279378739806485116e-912j 1.02e-236, 1.02e-236j
0.81203591675445274504 + 2.4470207158726042781e-915j 3.37e-239, 3.37e-239j
0.84648809715906767396 - 3.083111546394732195e-913j 1.3e-238, 1.3e-238j
-0.95151371618655174505 + 7.3086552410194718067e-917j 5.72e-237, 5.72e-237j
-0.81203591675445274504 - 2.6326363016369202698e-920j 3.28e-239, 3.28e-239j
-0.96865830675279425645 - 2.7967158074613431247e-918j 1.06e-236, 1.06e-236j
0.87783567338819181439 + 6.2115349442887970359e-916j 4.03e-238, 4.03e-238j
0.77459666924148337704 + 7.3384224944908851812e-925j 7.33e-240, 7.33e-240j
-0.17101852249474448773 + 1.8288224316692655707e-940j 7.66e-251, 7.66e-251j
-0.73426377039106497216 + 5.1777079105351616766e-938j 1.56e-240, 1.56e-240j
-0.69113262396834268581 - 8.8087911446740278767e-940j 2.68e-241, 2.68e-241j
0.98189373966174310941 + 8.3193746033073015926e-934j 1.79e-236, 1.79e-236j
0.73426377039106497216 + 9.9419328704384658094e-957j 1.58e-240, 1.58e-240j
0.54665888028373232627 - 9.2179789295651795563e-964j 5.98e-244, 5.98e-244j
-0.14715303420776064898 - 3.5123921494269231799e-970j 3.1e-251, 3.1e-251j
-0.64533232741799124195 - 7.3868152942782584946e-966j 3.98e-242, 3.98e-242j
-0.77459666924148337704 - 9.2665033751846351449e-963j 7.96e-240, 7.96e-240j
0.22617367918814454639 + 3.8287343770830734687e-971j 4.31e-250, 4.31e-250j
0.69113262396834268581 + 4.2003911945383138571e-963j 2.57e-241, 2.57e-241j
0.96865830675279425645 + 5.1964788677880177538e-976j 1.12e-236, 1.12e-236j
-0.59706738604131558719 + 1.4994408330700202206e-989j 5.63e-243, 5.63e-243j
-0.49455577980099296881 + 5.7469941782206314902e-993j 6.42e-245, 6.42e-245j
0.060379947809744553847 + 9.7996540604297006017e-999j 3.27e-254, 3.27e-254j
0.59706738604131558719 - 3.44559160657478407e-989j 4.92e-243, 4.92e-243j
0.17101852249474448773 - 4.4564491143266509311e-997j 8.18e-251, 8.18e-251j
-0.33324545045981175859 + 8.7465924086407378632e-996j 5.12e-248, 5.12e-248j
-0.54665888028373232627 + 7.7362474388493573765e-995j 6.08e-244, 6.08e-244j
-0.12051321105334727754 + 2.2041601290204316327e-999j 3.56e-252, 3.56e-252j
0.38736385932378655649 + 2.2070914957135757177e-993j 5.52e-247, 5.52e-247j
0.44128701576964658439 - 9.6627505269877427119e-992j 6.02e-246, 6.02e-246j
5.3477127151332812392e-1012 - 1.3389655799366763666e-1011j 7.93e-1010, 7.93e-1010j
-0.44128701576964658439 - 3.2193624361619418537e-994j 5.85e-246, 5.85e-246j
-0.27944386352261028131 + 1.0175846287136671657e-996j 4.43e-249, 4.43e-249j
0.14715303420776064898 + 3.9146054916383681636e-998j 2.51e-251, 2.51e-251j
0.49455577980099296881 + 1.1761975001661225339e-991j 6.55e-245, 6.55e-245j
0.12051321105334727754 - 2.848228660952966793e-999j 3.79e-252, 3.79e-252j
-0.22617367918814454639 - 3.7559894689774359214e-998j 4.62e-250, 4.62e-250j
-0.38736385932378655649 - 2.0214783561682826402e-995j 5.52e-247, 5.52e-247j
-0.060379947809744553847 - 7.5659051886693144643e-1002j 3.23e-254, 3.23e-254j
0.33324545045981175859 - 1.7626054732171635505e-995j 5.07e-248, 5.07e-248j
0.27944386352261028131 - 2.864826413648778255e-996j 4.48e-249, 4.48e-249j

Weights

Weight (ball center) Error (ball radius)
0.0040176984325220973381 - 5.4380788173705619055e-853j 1.72e-51, 2.75e-165j
0.011280115131044668763 + 2.3474270867604232699e-852j 1.01e-51, 1.61e-165j
0.022828774477648776837 - 2.8471828462537655116e-852j 5.05e-52, 8.1e-166j
0.0012937720931858497773 - 6.1864702606135030061e-850j 3.29e-53, 5.27e-167j
0.019078356223886945489 + 6.4691017036032892238e-851j 1.88e-53, 3.01e-167j
0.022828774477648776837 - 4.8273887916790249173e-851j 1.23e-53, 1.97e-167j
0.0074789788411870403592 - 2.5558972868605230907e-853j 1.13e-52, 1.81e-166j
0.026389464745564009762 + 1.8538085482770990539e-852j 3.95e-54, 6.34e-168j
0.0074789788411870403592 - 3.3166525794478853872e-850j 7.25e-54, 1.16e-167j
0.0040176984325220973381 + 8.4411872751706029579e-850j 1.54e-53, 2.46e-167j
0.026389464745564009762 + 3.9458300595700279465e-851j 4.07e-55, 6.53e-169j
0.047075295862928102142 - 4.0478164159104521684e-851j 1.59e-57, 2.55e-171j
0.029745997640958017509 - 2.4698741377130439233e-852j 1.4e-55, 2.24e-169j
0.032922616047535359317 + 2.9636388454745018407e-852j 2.62e-56, 4.21e-170j
0.0012937720931858497773 + 1.8984453602730443616e-852j 1.1e-54, 1.77e-168j
0.035962485037455604115 - 3.1427587274599409382e-851j 5.23e-58, 8.38e-172j
0.032922616047535359317 + 3.2298484853488094734e-851j 1.18e-57, 1.89e-171j
0.019078356223886945489 + 4.2487387323138201535e-852j 7e-56, 1.12e-169j
0.035962485037455604115 - 3.5650253026330518386e-852j 1.24e-58, 1.99e-172j
0.015195780912532016749 - 5.5823067775099551455e-852j 1.14e-55, 1.82e-169j
0.029745997640958017509 - 3.4697157693360046366e-851j 1.15e-58, 1.85e-172j
0.038900882893046102933 + 3.1716432709852467559e-851j 5.15e-60, 8.26e-174j
0.060894698215360563257 + 3.0744082528067006356e-849j 7.37e-64, 1.18e-177j
0.041749518179243502306 - 5.4227026934351386218e-852j 5.25e-61, 8.42e-175j
0.044491977950426821612 + 6.9285372628111405019e-852j 1.05e-61, 1.69e-175j
0.011280115131044668763 + 1.6529766540852662876e-850j 1.03e-59, 1.65e-173j
0.041749518179243502306 - 3.3111741609746715388e-851j 6.84e-62, 1.1e-175j
0.051340056238131434229 - 6.0767161469851461553e-851j 2.56e-64, 4.1e-178j
-0.014690263023767041262 - 5.1233449277707001926e-849j 2.79e-65, 4.48e-179j
0.047075295862928102142 - 9.1580435222081727781e-852j 1.13e-63, 1.81e-177j
0.038900882893046102933 + 4.3537862526592697436e-852j 1.04e-61, 1.66e-175j
0.053327686562126791939 - 1.0822538625326507518e-849j 1.57e-67, 2.51e-181j
0.044491977950426821612 + 3.5841422701688277077e-851j 9.21e-64, 1.48e-177j
0.015195780912532016749 - 9.6806224300970296454e-851j 8.18e-62, 1.31e-175j
0.049401342762070116204 + 1.2651303395925956986e-851j 3.04e-65, 4.88e-179j
0.052776089641081016622 + 2.8566748199641116384e-851j 8.52e-67, 1.36e-180j
0.060019929418447012772 - 1.2576423645175842197e-849j 6.68e-69, 1.07e-182j
0.049401342762070116204 + 4.8121952090384138728e-851j 1.96e-66, 3.14e-180j
0.060894698215360563257 + 4.3076812505004164123e-849j 8e-69, 1.28e-182j
0.05405213283963196628 - 1.5351737672566893808e-850j 3.73e-69, 5.98e-183j
0.051340056238131434229 - 1.8445407560758128335e-851j 2.58e-67, 4.14e-181j
0.0629241968468818835 + 3.1914923885206055656e-849j 1.1e-68, 1.76e-182j
0.054097562070695104487 + 1.8272927372797939356e-850j 2.37e-70, 3.8e-184j
0.053675151383444314146 - 1.1841940996734672221e-850j 3.72e-70, 5.97e-184j
0.060574547817963754384 + 9.4414882530487611526e-850j 2.6e-70, 4.17e-184j
0.053675151383444314146 - 4.7064523875603881872e-851j 3.34e-70, 5.36e-184j
0.053482428667750045627 + 3.0694611179208884915e-850j 1.57e-70, 2.51e-184j
-0.014690263023767041262 - 6.8435653912995515659e-849j 9.29e-71, 1.49e-184j
0.052776089641081016622 + 8.2004990809627962371e-851j 7.64e-72, 1.22e-185j
0.0629241968468818835 + 4.0431854311841070394e-849j 5.47e-71, 8.77e-185j
0.053327686562126791939 - 6.9055486937151688387e-850j 1.36e-71, 2.19e-185j
0.054097562070695104487 + 8.2389843570728675066e-851j 3.2e-72, 5.13e-186j
0.060019929418447012772 - 1.1175497176506733217e-849j 6.51e-72, 1.04e-185j
0.05405213283963196628 - 3.0173554757856967283e-850j 7.6e-74, 1.22e-187j
0.053482428667750045627 + 5.3746933535736195969e-850j 1.47e-73, 2.35e-187j

Download

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