Rule: Q[22, 24, 48]

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.

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)
0.99985359134909298911 - 2.1234271494196706292e-1816j 1.08e-475, 1.08e-475j
-0.98464374446473086908 + 7.3077297128508383699e-1849j 1.59e-475, 1.59e-475j
-0.92695677218717400052 - 6.7387253046519842641e-1851j 7.48e-477, 7.48e-477j
0.99429458548239929207 + 2.00688044037101673e-1846j 2.39e-475, 2.39e-475j
0.94535958067189815581 + 8.5280566949662954939e-1860j 1.29e-475, 1.29e-475j
0.93943618611899883322 + 8.8130931337931660532e-1861j 5.12e-476, 5.12e-476j
-0.99725631199436823609 - 1.2332057925246508955e-1858j 2.65e-475, 2.65e-475j
-0.91334156012273284742 - 2.236689234611533374e-1863j 1.68e-477, 1.68e-477j
0.97795472485101194583 - 1.1323026119613288779e-1859j 1.17e-475, 1.17e-475j
-0.9609956372030518928 - 4.5846196789720653307e-1864j 8.1e-476, 8.1e-476j
0.88274742314088334936 + 6.1491338036650444521e-1868j 1.16e-478, 1.16e-478j
0.95078620158894464521 - 5.1210375935269230724e-1865j 1.19e-475, 1.19e-475j
-0.71917455482218440793 - 8.8343233194804085005e-1874j 2.74e-484, 2.74e-484j
-0.88274742314088334936 - 4.1941720587877510289e-1869j 1.06e-478, 1.06e-478j
-0.99905156467873088415 - 6.3551262604151938569e-1862j 2.48e-475, 2.48e-475j
0.86581257772030013654 + 1.6818428373359025116e-1869j 2.83e-479, 2.83e-479j
0.91334156012273284742 - 3.1643882262886363497e-1866j 1.82e-477, 1.82e-477j
0.9609956372030518928 + 1.5287756354465996053e-1863j 8.21e-476, 8.21e-476j
-0.76586841916196380677 + 2.6846039834821158814e-1876j 1.08e-482, 1.08e-482j
-0.97006049783542872712 - 9.0822145341184214625e-1868j 9.08e-476, 9.08e-476j
0.89859912908272990619 + 1.6614318149158059293e-1871j 4.51e-478, 4.51e-478j
0.76586841916196380677 + 3.962440355637313896e-1876j 1.08e-482, 1.08e-482j
-0.94535958067189815581 - 6.0066910829640650043e-1869j 1.26e-475, 1.26e-475j
-0.80880442467257749786 - 3.8566630266338439061e-1876j 3.07e-481, 3.07e-481j
-0.787816805979208162 + 2.3706889207404840035e-1877j 6.14e-482, 6.14e-482j
-0.99009559261565633137 + 7.3143123669018185243e-1868j 1.89e-475, 1.89e-475j
0.74297908326598811891 + 1.5203042884746281006e-1878j 1.74e-483, 1.74e-483j
0.84782483332065874039 - 9.7881481105280723695e-1873j 7.07e-480, 7.07e-480j
-0.97795472485101194583 + 1.7456135780091691299e-1868j 1.14e-475, 1.14e-475j
-0.64261281216735728096 - 5.6590295264327124299e-1881j 6.52e-487, 6.52e-487j
0.97006049783542872712 + 1.2318775730878791276e-1867j 9.32e-476, 9.32e-476j
0.80880442467257749786 + 1.7868771106062368446e-1900j 3.04e-481, 3.04e-481j
0.71917455482218440793 + 3.1908045603824825292e-1905j 2.72e-484, 2.72e-484j
-0.95078620158894464521 + 3.2001755042544930212e-1898j 1.26e-475, 1.26e-475j
-0.66895413370940206568 - 3.9514954762894508424e-1908j 5.52e-486, 5.52e-486j
-0.74297908326598811891 - 3.5253365143745358355e-1906j 1.77e-483, 1.77e-483j
-0.99985359134909298911 + 1.8341300570257407094e-1896j 1.02e-475, 1.02e-475j
0.64261281216735728096 - 1.2679062188074232204e-1908j 6.58e-487, 6.58e-487j
0.98464374446473086908 - 8.1045088993013856716e-1895j 1.47e-475, 1.47e-475j
-0.82881374149829671237 - 9.285018669207800091e-1941j 1.4e-480, 1.4e-480j
-0.58764040350691159296 + 3.4530164029898112955e-1949j 8.01e-489, 8.01e-489j
-0.89859912908272990619 + 9.0069011483507873651e-1937j 4.37e-478, 4.37e-478j
0.787816805979208162 - 9.6293109575161979571e-1935j 5.86e-482, 5.86e-482j
0.61549810612741687938 + 5.2527982309292789029e-1956j 7.32e-488, 7.32e-488j
0.99725631199436823609 + 5.6706975988057910962e-1942j 2.63e-475, 2.63e-475j
-0.61549810612741687938 + 8.4917950236785438194e-1988j 7.51e-488, 7.51e-488j
-0.86581257772030013654 + 4.2540973824956945136e-1980j 2.77e-479, 2.77e-479j
0.92695677218717400052 + 3.4162742019148119676e-1974j 7.62e-477, 7.62e-477j
0.4998892392874274185 + 5.9726580584736192313e-2007j 5.49e-492, 5.49e-492j
0.82881374149829671237 + 4.4779571132025832356e-1990j 1.36e-480, 1.36e-480j
-0.43824959396135745426 + 7.6901470642295594697e-2013j 2.94e-494, 2.94e-494j
-0.52980585625888353667 - 4.1581331778863294429e-2009j 6.77e-491, 6.77e-491j
-0.10445350165318807797 - 8.6582240973109798404e-2025j 5.78e-507, 5.78e-507j
0.58764040350691159296 - 1.4151927458692250608e-2006j 7.49e-489, 7.49e-489j
0.55906702237741443818 + 9.0269183538923648461e-2008j 7.96e-490, 7.96e-490j
-0.93943618611899883322 + 3.1260665641605760789e-1992j 5.66e-476, 5.66e-476j
-0.4998892392874274185 + 1.8638173834781174777e-2010j 5.24e-492, 5.24e-492j
-0.69448726318668278005 + 7.8724133282920894352e-2003j 3.78e-485, 3.78e-485j
0.20786042668822128548 - 3.7745513607017454387e-2021j 6.13e-503, 6.13e-503j
0.40661625810907595575 - 5.4506366068109606791e-2014j 2.08e-495, 2.08e-495j
-0.84782483332065874039 - 1.0107372080945558368e-1996j 7.13e-480, 7.13e-480j
-0.55906702237741443818 - 2.2926245402022978458e-2007j 7.1e-490, 7.1e-490j
-0.40661625810907595575 - 3.556101642548221162e-2013j 2.06e-495, 2.06e-495j
0.52980585625888353667 + 3.083482477962203051e-2009j 6.49e-491, 6.49e-491j
0.43824959396135745426 + 2.250372665878646611e-2012j 3.03e-494, 3.03e-494j
0.66895413370940206568 + 1.1758815588621849322e-2004j 5.43e-486, 5.43e-486j
-0.13908650899000955713 + 9.0833113280346810133e-2024j 1.29e-505, 1.29e-505j
-0.3744990979296158698 + 5.3708576576379515886e-2015j 1.33e-496, 1.33e-496j
0.99905156467873088415 + 7.6565354302667521976e-1991j 2.25e-475, 2.25e-475j
0.69448726318668278005 + 8.262429298946585219e-2034j 4.02e-485, 4.02e-485j
0.3744990979296158698 + 4.1644961024220553926e-2045j 1.3e-496, 1.3e-496j
0.99009559261565633137 - 2.8463676911292713817e-2039j 1.97e-475, 1.97e-475j
-0.34193582089208422516 - 3.8743699962316100914e-2068j 7.59e-498, 7.59e-498j
-0.46935583798675702641 + 9.6337327059034927044e-2064j 4.21e-493, 4.21e-493j
-0.0026780668333038090376 - 1.3860147269437588166e-2082j 2.98e-511, 2.98e-511j
0.34193582089208422516 + 3.8834384656900667303e-2069j 7.6e-498, 7.6e-498j
0.46935583798675702641 + 7.3142344439240875609e-2065j 4.44e-493, 4.44e-493j
-0.99429458548239929207 - 6.7169660392987745992e-2075j 2.33e-475, 2.33e-475j
-0.2755969500421847707 - 1.5448726258999377131e-2104j 2.57e-500, 2.57e-500j
-0.1735756039094188978 - 4.9584746585837233278e-2109j 2.63e-504, 2.63e-504j
0.069739273319722221214 - 4.4334424852595862158e-2112j 2.71e-508, 2.71e-508j
0.30895849732253085603 + 5.5766654348608855977e-2104j 4.82e-499, 4.82e-499j
0.10445350165318807797 + 6.4276861420755636628e-2111j 5.23e-507, 5.23e-507j
-0.20786042668822128548 + 7.4794050194877582452e-2107j 6.09e-503, 6.09e-503j
-0.30895849732253085603 - 3.2229186499919634503e-2103j 4.62e-499, 4.62e-499j
0.0026780668333038090376 - 2.8775667400643948912e-2115j 2.98e-511, 2.98e-511j
0.2755969500421847707 + 2.0733720683428860664e-2104j 2.56e-500, 2.56e-500j
0.1735756039094188978 - 1.4878436002896906787e-2108j 2.49e-504, 2.49e-504j
-0.069739273319722221214 - 8.8918994702894101904e-2114j 2.54e-508, 2.54e-508j
-0.24188408822578752492 + 5.6808045064058819935e-2106j 1.24e-501, 1.24e-501j
-0.035038080872604644366 + 7.7837545572099134342e-2113j 1.27e-509, 1.27e-509j
0.13908650899000955713 + 9.0840290366497397577e-2110j 1.19e-505, 1.19e-505j
0.24188408822578752492 + 2.2335241287667273626e-2105j 1.28e-501, 1.28e-501j
0.035038080872604644366 - 8.3013344753035789784e-2113j 1.27e-509, 1.27e-509j

Weights

Weight (ball center) Error (ball radius)
0.0004038439274359025713 + 1.9692385455905314255e-1816j 2.68e-125, 4.88e-353j
0.0060748619049288100232 + 1.8015037397613803877e-1819j 7.06e-126, 1.29e-353j
0.013048124442528593322 - 4.3693798486739132023e-1819j 7.06e-126, 1.29e-353j
0.0035742376921595037326 - 5.3630487457109058159e-1817j 9.24e-126, 1.68e-353j
1.0011469911364262063e-05 + 7.6182153368190471495e-1817j 1.68e-126, 3.05e-354j
0.011909127676398585605 - 4.2358791755159490359e-1817j 1.22e-126, 2.23e-354j
0.0023602552622522830976 - 1.3736611788224075011e-1819j 6.3e-129, 1.15e-356j
0.01418098596831947356 + 2.5809207451637646704e-1819j 6.92e-128, 1.26e-355j
0.0072976190853501938802 + 1.9599455213235351535e-1817j 1.18e-127, 2.15e-355j
0.0096405042722834585756 - 4.7117561170294245502e-1819j 6.95e-129, 1.27e-356j
0.016398132403803560273 - 2.2559467022186673613e-1818j 6.37e-129, 1.16e-356j
0.01077479875745625354 - 5.5591158634499789877e-1817j 3.12e-127, 5.68e-355j
0.024251800946234934909 + 5.7452903739175053431e-1820j 4.92e-131, 8.96e-359j
0.016398132403803560273 + 1.4032993286702688254e-1819j 1.13e-129, 2.07e-357j
0.0012577330658140786106 + 1.0772611072888191238e-1819j 1.54e-129, 2.81e-357j
0.017466434385246567178 + 1.595550064507009872e-1818j 8.3e-130, 1.51e-357j
0.01418098596831947356 - 5.7076512780754376669e-1818j 4.1e-129, 7.46e-357j
0.0096405042722834585756 + 2.3776453367770221885e-1817j 1.76e-128, 3.2e-356j
0.022422579614201723251 + 6.4535575565678417597e-1820j 8.14e-133, 1.48e-360j
0.0084848638648904803785 + 2.9072280293313372133e-1819j 2.88e-131, 5.23e-359j
0.015300851940748491552 + 3.4104841357516425576e-1818j 1.16e-129, 2.12e-357j
0.022422579614201723251 - 4.870047327024001742e-1819j 1.28e-133, 2.32e-361j
1.0011469911364262063e-05 - 2.1341985232110419904e-1818j 2.59e-131, 4.71e-359j
0.020501444388395792395 + 7.649797168160399527e-1820j 1.14e-133, 2.07e-361j
0.021470956584270060397 - 6.9747980432224498288e-1820j 1.25e-133, 2.27e-361j
0.0048259880535885668793 - 1.606984675908441523e-1819j 4.25e-132, 7.73e-360j
0.023351811291186294957 + 4.1053757596304190746e-1819j 4.69e-136, 8.54e-364j
0.018504061470398572652 - 1.1847625611284055392e-1818j 4.18e-134, 7.62e-362j
0.0072976190853501938802 - 2.1701084459710328627e-1819j 2.93e-132, 5.34e-360j
0.026733452623208292555 - 5.2764873704351457358e-1820j 1.28e-138, 2.33e-366j
0.0084848638648904803785 - 1.9222540461685641479e-1817j 4.63e-133, 8.43e-361j
0.020501444388395792395 - 7.2420451812595841813e-1819j 1.53e-135, 2.78e-363j
0.024251800946234934909 - 3.5187223039167929094e-1819j 2.04e-137, 3.71e-365j
0.01077479875745625354 + 1.3983684008767083509e-1818j 4.94e-133, 9e-361j
0.025943360158314819889 + 5.3691409957972749417e-1820j 1.16e-138, 2.11e-366j
0.023351811291186294957 - 6.0508756469365397698e-1820j 5.74e-137, 1.05e-364j
0.0004038439274359025713 - 4.2882936415150618949e-1820j 5.11e-134, 9.3e-362j
0.026733452623208292555 + 2.4259417568087273871e-1819j 5.15e-142, 9.38e-370j
0.0060748619049288100232 - 2.3505031965119835123e-1817j 5.13e-137, 9.34e-365j
0.019513920233841103119 - 8.5391932595859512286e-1820j 7.72e-137, 1.41e-364j
0.028219999726012843014 - 5.2412727447099409562e-1820j 7.12e-142, 1.3e-369j
0.015300851940748491552 - 1.8189904521559348029e-1819j 1.41e-135, 2.56e-363j
0.021470956584270060397 + 5.8804136119406717799e-1819j 3.9e-139, 7.11e-367j
0.027490918840580818092 - 2.2004287033889583562e-1819j 7.7e-144, 1.4e-371j
0.0023602552622522830976 + 1.056240769432139242e-1816j 2.42e-138, 4.4e-366j
0.027490918840580818092 + 5.235682379929930981e-1820j 3.21e-142, 5.84e-370j
0.017466434385246567178 - 1.1463419956244626523e-1819j 3.35e-138, 6.1e-366j
0.013048124442528593322 + 1.1549154642743941345e-1817j 6.17e-137, 1.12e-364j
0.030231977093603788846 - 1.6625170213331903194e-1819j 2.14e-147, 3.9e-375j
0.019513920233841103119 + 9.1296524034002781175e-1819j 4.91e-139, 8.94e-367j
0.031377346080437914693 + 6.0494327260835560783e-1820j 1.13e-147, 2.05e-375j
0.029594793260108478193 - 5.3898714187778188238e-1820j 1.11e-145, 2.03e-373j
0.034684546121230037932 + 2.6398526243812572069e-1819j 1.76e-151, 3.2e-379j
0.028219999726012843014 + 2.0184917059992353895e-1819j 5.44e-146, 9.9e-374j
0.028922183884603042122 - 1.8715180979557251993e-1819j 7.73e-147, 1.41e-374j
0.011909127676398585605 + 1.3196626498335420799e-1818j 2.03e-138, 3.7e-366j
0.030231977093603788846 + 5.5422785052392042278e-1820j 4.26e-147, 7.75e-375j
0.025116560693480961373 - 5.5219987548158975407e-1820j 1.18e-142, 2.15e-370j
0.034163230585000996202 + 1.9079544848095624032e-1819j 1.31e-153, 2.38e-381j
0.031882058370512550463 + 1.5241521429878985382e-1819j 1.01e-151, 1.84e-379j
0.018504061470398572652 + 9.7483403130137286347e-1820j 1.95e-141, 3.54e-369j
0.028922183884603042122 + 5.2917386164670412194e-1820j 5.78e-146, 1.05e-373j
0.031882058370512550463 - 6.4287474993262568686e-1820j 2.75e-150, 5.01e-378j
0.029594793260108478193 + 1.7540064809680275164e-1819j 8.43e-150, 1.53e-377j
0.031377346080437914693 - 1.5490823628692409145e-1819j 5.52e-152, 1.01e-379j
0.025943360158314819889 - 2.7077904674208224246e-1819j 2.22e-148, 4.04e-376j
0.03457121874387158178 - 1.9341157670266301378e-1819j 9.38e-156, 1.71e-383j
0.032345974632412271594 + 6.9130262818175264773e-1820j 1.43e-152, 2.6e-380j
0.0012577330658140786106 - 2.6848767769476495081e-1816j 2.66e-146, 4.85e-374j
0.025116560693480961373 + 3.0639095493214155811e-1819j 7.83e-149, 1.43e-376j
0.032345974632412271594 - 1.5192880776339517122e-1819j 5e-155, 9.1e-383j
0.0048259880535885668793 + 3.2771246767129111695e-1817j 3.17e-146, 5.77e-374j
0.032775294833025042735 - 7.5262257692265413838e-1820j 1.66e-155, 3.02e-383j
0.030827440163356265392 - 5.7583588141182822303e-1820j 1.46e-152, 2.66e-380j
0.01775788149720781985 - 5.5967786786496132492e-1818j 1.13e-159, 2.06e-387j
0.032775294833025042735 + 1.534934988041149186e-1819j 7.58e-157, 1.38e-384j
0.030827440163356265392 + 1.594773024688635633e-1819j 5.9e-154, 1.07e-381j
0.0035742376921595037326 + 1.4950353131802626672e-1819j 8.23e-150, 1.5e-377j
0.033543212586883825465 - 9.3153991783792371275e-1820j 2.75e-158, 5.01e-386j
0.034396862315646256754 + 1.5196260380866362263e-1819j 3.04e-159, 5.54e-387j
0.034730999494177106889 + 4.6776022035306511035e-1819j 2.48e-161, 4.51e-389j
0.03317447818593543332 - 1.5735050708502641264e-1819j 1.25e-159, 2.28e-387j
0.034684546121230037932 - 3.255760202765860163e-1819j 1.5e-161, 2.72e-389j
0.034163230585000996202 - 1.2511959684867555508e-1819j 2.55e-160, 4.63e-388j
0.03317447818593543332 + 8.3062109777710168055e-1820j 2.91e-159, 5.3e-387j
0.01775788149720781985 + 5.62684068274846359e-1818j 3.02e-161, 5.51e-389j
0.033543212586883825465 + 1.6404862928008518965e-1819j 7.62e-162, 1.39e-389j
0.034396862315646256754 - 2.1580794672883263596e-1819j 1.12e-162, 2.04e-390j
0.034730999494177106889 - 4.0676269702834355524e-1819j 1.88e-162, 3.43e-390j
0.033875784687070041834 + 1.0658053375220464917e-1819j 5.04e-162, 9.17e-390j
0.034615476721675162292 + 8.3220357097144022476e-1819j 1.52e-162, 2.76e-390j
0.03457121874387158178 + 2.5591615326732463346e-1819j 7.92e-164, 1.44e-391j
0.033875784687070041834 - 1.7460473557837209744e-1819j 4.85e-164, 8.86e-392j
0.034615476721675162292 - 8.9264790609156529572e-1819j 2.96e-163, 5.39e-391j

Download

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