Rule: Q[6, 9, 76]

Type

This rule is of Hermite (physicists') 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)
11.117379349101090879 - 8.8182207926808241207e-1724j 7.32e-494, 7.32e-494j
-9.1778579510011689174 + 2.2986100024671357011e-1718j 1.13e-490, 1.13e-490j
9.8872357581921909682 - 6.061681478386962236e-1725j 1.39e-491, 1.39e-491j
-11.613394920050297114 - 1.9425997681479375708e-1728j 4.96e-495, 4.96e-495j
10.675586251719491427 - 7.2299351948279588547e-1727j 6e-493, 6e-493j
-9.5248777996633493413 + 5.4858401951720602932e-1722j 4.21e-491, 4.21e-491j
-7.0152454274859507744 + 4.4670520899745857862e-1728j 8.98e-490, 8.98e-490j
-1.1082012875144997416 + 1.2700269230563041478e-1748j 4.66e-503, 4.66e-503j
-1.9072865624118656773 - 1.7748027552330010111e-1744j 1.22e-499, 1.22e-499j
3.9268135162497144207 + 3.7601927495997999951e-1738j 8.19e-493, 8.19e-493j
1.1082012875144997416 - 2.0772706960237342588e-1748j 4.57e-503, 4.57e-503j
-8.204814510767702279 + 1.0307270351762533143e-1733j 6.1e-490, 6.1e-490j
-1.7281759088743055938 - 3.4036094257631357939e-1752j 2.65e-500, 2.65e-500j
-1.5478881666047928113 + 1.2652285742324868111e-1752j 3.66e-501, 3.66e-501j
-8.5196024914362764207 + 2.5551300265339466412e-1740j 4.01e-490, 4.01e-490j
10.26883129731562295 + 1.4580221192481660776e-1755j 3.29e-492, 3.29e-492j
-12.213895245183783151 - 4.0570775175456748706e-1758j 1.34e-496, 1.34e-496j
9.5248777996633493413 + 1.7739731991850281007e-1753j 4.16e-491, 4.16e-491j
8.8434379291434994962 + 7.4915307205918858391e-1753j 2.27e-490, 2.27e-490j
5.9054847393912450345 - 2.803959362510723883e-1752j 2.5e-490, 2.5e-490j
-7.8978681142187515532 + 1.3998403429820539942e-1750j 8.12e-490, 8.12e-490j
2.3506049736744922228 + 1.1249438528487288912e-1777j 3.65e-498, 3.65e-498j
7.3038066988064421106 - 8.3742006903796429613e-1768j 1.05e-489, 1.05e-489j
-6.1770435023858571681 + 7.1347017451077855527e-1768j 3.94e-490, 3.94e-490j
11.613394920050297114 + 6.4803937595461117666e-1791j 5.3e-495, 5.3e-495j
5.3724246076122737297 + 4.1793575992596767119e-1786j 6.99e-491, 6.99e-491j
-7.5977957280120946766 + 7.3294459091605592043e-1784j 9.54e-490, 9.54e-490j
-5.1106076595385866946 - 3.7892029563351043032e-1805j 3.46e-491, 3.46e-491j
6.452292554471648081 - 4.0432143852062228744e-1813j 6.45e-490, 6.45e-490j
-11.117379349101090879 - 3.911585979165021509e-1819j 7.15e-494, 7.15e-494j
-10.26883129731562295 + 2.0889604620768159746e-1815j 3.02e-492, 3.02e-492j
8.204814510767702279 - 1.0647342818942154476e-1814j 6.19e-490, 6.19e-490j
-9.8872357581921909682 - 1.1506934690273557488e-1814j 1.32e-491, 1.32e-491j
-10.675586251719491427 - 1.5438526586807667475e-1819j 6.85e-493, 6.85e-493j
3.0701613138889128067 - 2.7579529555160451122e-1828j 9.47e-496, 9.47e-496j
-6.452292554471648081 - 2.1306859145647206138e-1821j 5.91e-490, 5.91e-490j
1.7281759088743055938 - 5.6026698396050873723e-1850j 2.7e-500, 2.7e-500j
5.1106076595385866946 + 2.7170967581761105205e-1840j 3.63e-491, 3.63e-491j
4.1108152807287541899 + 1.936907804626192256e-1841j 1.55e-492, 1.55e-492j
-3.5517547697054951901 - 3.1197139522620385929e-1841j 4.63e-494, 4.63e-494j
8.5196024914362764207 + 1.6841724901415645282e-1838j 4.12e-490, 4.12e-490j
-3.7709163338688759015 + 9.3194158334458278719e-1841j 3.06e-493, 3.06e-493j
-8.8434379291434994962 + 6.1922564332093968078e-1843j 2.42e-490, 2.42e-490j
2.1202214064344157181 - 1.2570097676771274267e-1863j 6.64e-499, 6.64e-499j
2.587732052106509866 - 2.1294191517843772762e-1861j 2.08e-497, 2.08e-497j
12.213895245183783151 - 3.774085371216380527e-1862j 1.31e-496, 1.31e-496j
7.5977957280120946766 + 2.9194233693824177104e-1853j 9.32e-490, 9.32e-490j
6.7315621736699192904 + 3.6377396540462665504e-1853j 7.77e-490, 7.77e-490j
1.5478881666047928113 - 7.0835349696184028527e-1870j 3.73e-501, 3.73e-501j
3.3125307911686668706 - 4.2819164987692844325e-1862j 7.27e-495, 7.27e-495j
-7.3038066988064421106 - 2.0883461088602990598e-1856j 1.02e-489, 1.02e-489j
-0.95452011014285350763 + 1.0254056330561999558e-1884j 1.65e-503, 1.65e-503j
5.6373462354686513898 - 2.7634526879285442545e-1871j 1.4e-490, 1.4e-490j
7.0152454274859507744 + 8.235198336569254469e-1872j 9.74e-490, 9.74e-490j
0.66057200447970670507 + 3.6932829256959982504e-1887j 6.05e-506, 6.05e-506j
-4.5968791750767061343 + 1.188932614148219342e-1870j 6.25e-492, 6.25e-492j
-1.3358490740136969497 + 1.3841469448631779514e-1891j 3.64e-502, 3.64e-502j
-4.1108152807287541899 + 1.8013715297967775495e-1878j 1.6e-492, 1.6e-492j
6.1770435023858571681 - 7.7352608430968772748e-1887j 3.85e-490, 3.85e-490j
7.8978681142187515532 + 5.9060253550751110832e-1887j 8.5e-490, 8.5e-490j
4.5968791750767061343 + 3.7020948949237349348e-1895j 6.25e-492, 6.25e-492j
-2.8280939962445144939 + 1.0523023883837586013e-1892j 1.36e-496, 1.36e-496j
9.1778579510011689174 + 5.1595514143622331442e-1893j 1.06e-490, 1.06e-490j
-5.6373462354686513898 + 4.5510366781909477795e-1891j 1.33e-490, 1.33e-490j
-3.0701613138889128067 - 5.1086144814843275034e-1915j 9.66e-496, 9.66e-496j
-6.7315621736699192904 - 3.3550212767572527768e-1908j 7.66e-490, 7.66e-490j
3.5517547697054951901 - 2.4046529930385014389e-1924j 4.76e-494, 4.76e-494j
-2.1202214064344157181 - 3.043927362696518637e-1929j 6.56e-499, 6.56e-499j
-0.8952681375077315078 - 6.9244215262631031928e-1934j 7.09e-504, 7.09e-504j
-4.8519460488273854963 - 8.0122784082075658305e-1920j 1.46e-491, 1.46e-491j
0.43607741192761650868 + 2.7446199251218853732e-1943j 1.54e-507, 1.54e-507j
1.3358490740136969497 + 4.7222782166327844434e-1939j 3.47e-502, 3.47e-502j
4.3471301541829114048 - 1.8777448117452501485e-1928j 3.03e-492, 3.03e-492j
-0.66057200447970670507 + 3.1800768812485384339e-1941j 6.63e-506, 6.63e-506j
-2.587732052106509866 + 9.8572465936839345068e-1933j 2.22e-497, 2.22e-497j
1.9072865624118656773 + 2.7326674054965066372e-1935j 1.35e-499, 1.35e-499j
4.8519460488273854963 - 3.3804263030118100284e-1928j 1.47e-491, 1.47e-491j
-4.3471301541829114048 - 6.3757781708130485077e-1926j 2.96e-492, 2.96e-492j
-5.9054847393912450345 + 2.4655264956239874144e-1935j 2.36e-490, 2.36e-490j
-5.3724246076122737297 - 6.6779952395081027671e-1960j 7.25e-491, 7.25e-491j
2.8280939962445144939 - 8.5243853374550841845e-1971j 1.38e-496, 1.38e-496j
0.21635554412511755427 + 5.1274766435229754483e-1983j 7.68e-509, 7.68e-509j
0.95452011014285350763 + 1.0182791146234286748e-1977j 1.6e-503, 1.6e-503j
-3.9268135162497144207 + 2.1333634115442635608e-1971j 8.87e-493, 8.87e-493j
-0.43607741192761650868 + 3.5384794988942074412e-1985j 1.96e-507, 1.96e-507j
-3.3125307911686668706 + 2.1327357573016990415e-1974j 7.2e-495, 7.2e-495j
0.8952681375077315078 - 1.1862597528925785061e-1981j 6.62e-504, 6.62e-504j
3.7709163338688759015 - 6.6588515121424573836e-1980j 2.86e-493, 2.86e-493j
-0.21635554412511755427 - 1.1725613093666391461e-1993j 7.68e-509, 7.68e-509j
-2.3506049736744922228 - 4.6619719628803131388e-1984j 3.75e-498, 3.75e-498j
-2.2676985561171093928e-2257 + 9.2135640011546222839e-2258j 2.23e-2255, 2.23e-2255j

Weights

Weight (ball center) Error (ball radius)
5.5107612463002270157e-55 - 4.5357863683551147663e-1766j 3.24e-160, 5.78e-403j
5.0277115770371718552e-38 + 1.1554915114136548673e-1754j 1.46e-153, 2.61e-396j
7.3369832107140594762e-44 + 4.190313805378053703e-1760j 3.05e-156, 5.45e-399j
8.0496857634547521438e-60 - 1.0498656786547892297e-1767j 1.9e-163, 3.4e-406j
7.6056836012836606948e-51 + 7.3401818976597088791e-1764j 6e-159, 1.07e-401j
7.9431202327205801377e-41 + 1.0018228151079082996e-1756j 3.04e-155, 5.43e-398j
6.8332082082551728718e-23 - 1.555957338599764855e-1747j 1.95e-145, 3.48e-388j
0.038758160319013020455 + 5.1640164744803206881e-1733j 1.2e-80, 2.15e-323j
0.002927442002278737574 + 2.5528840573456502263e-1734j 3.03e-100, 5.41e-343j
1.636600697359080156e-08 - 2.8029277205577467746e-1738j 1.69e-126, 3.02e-369j
0.038758160319013020455 + 4.0516543463599429959e-1733j 1.01e-81, 1.8e-324j
1.0173918129042983675e-30 - 1.2538968321239608641e-1751j 8.99e-151, 1.61e-393j
0.0047887405644800797763 - 5.8583296732683039016e-1734j 1.3e-97, 2.33e-340j
0.010180486966820036042 + 9.7621056341597038e-1734j 3.54e-94, 6.32e-337j
5.4033803607296835869e-33 + 1.0119851896025506906e-1752j 5.81e-152, 1.04e-394j
3.5472424892404193546e-47 - 6.8190788709783269352e-1762j 1.03e-160, 1.84e-403j
6.3892055268482988795e-66 + 5.1950059887360887853e-1771j 4.56e-168, 8.14e-411j
7.9431202327205801377e-41 - 1.857078369230466612e-1758j 7.9e-159, 1.41e-401j
2.0128029335321979615e-35 - 1.6964896912182621874e-1755j 2.5e-157, 4.47e-400j
1.0878515547341322243e-16 - 1.204855920842385444e-1744j 6.51e-146, 1.16e-388j
1.3921882455570943928e-28 + 1.4979142865418842163e-1750j 1.11e-152, 1.98e-395j
0.00052753150867431308205 + 1.5037721493714997166e-1735j 6.31e-118, 1.13e-360j
1.1165638046236163131e-24 + 1.9195890962241756005e-1749j 1.19e-152, 2.13e-395j
4.1425524721452930844e-18 + 7.9996744214501012716e-1745j 2.1e-147, 3.75e-390j
8.0496857634547521438e-60 + 1.2291962952917191986e-1768j 5.15e-168, 9.21e-411j
4.3346836662117232975e-14 - 5.8864436067537081615e-1743j 9.26e-144, 1.65e-386j
1.4247919879896972185e-26 - 1.6625658164076525991e-1749j 3.05e-152, 5.44e-395j
6.6651145203404667242e-13 + 1.3419938016016727807e-1741j 2.17e-143, 3.88e-386j
1.2990768550954689013e-19 - 1.8882826287761691762e-1746j 9.01e-150, 1.61e-392j
5.5107612463002270157e-55 + 4.7489951079493668201e-1765j 1.75e-167, 3.13e-410j
3.5472424892404193546e-47 + 1.2163570514866985968e-1760j 1.45e-164, 2.59e-407j
1.0173918129042983675e-30 - 7.0067404454816389779e-1753j 1.32e-159, 2.36e-402j
7.3369832107140594762e-44 - 1.1270529934080419667e-1758j 4.8e-163, 8.57e-406j
7.6056836012836606948e-51 - 9.7360904916914339463e-1763j 2.52e-166, 4.51e-409j
1.1029189351314742533e-05 - 5.8911419879223045998e-1737j 1.57e-136, 2.8e-379j
1.2990768550954689013e-19 - 1.0793018172193276416e-1745j 1.67e-152, 2.99e-395j
0.0047887405644800797763 - 4.0022794052160655713e-1734j 2.13e-123, 3.8e-366j
6.6651145203404667242e-13 + 3.8232894196757688453e-1742j 9.83e-149, 1.76e-391j
5.7129499401271374237e-09 + 6.7266802980389971304e-1739j 1.45e-143, 2.59e-386j
4.3980736060521185694e-07 - 2.3028431784142466602e-1737j 3.36e-142, 6.01e-385j
5.4033803607296835869e-33 + 3.7587575287844509975e-1754j 2.6e-162, 4.65e-405j
7.2301298005616728327e-08 + 1.3543640943322155745e-1737j 1.16e-143, 2.07e-386j
2.0128029335321979615e-35 - 9.1529147179160947171e-1754j 1.57e-160, 2.81e-403j
0.0014137480586794681255 - 5.0300292540028142694e-1735j 2.69e-131, 4.81e-374j
0.00016663754356262415823 - 4.814457268274533685e-1736j 2.07e-135, 3.7e-378j
6.3892055268482988795e-66 - 7.3695758561030817914e-1772j 2.74e-178, 4.89e-421j
1.4247919879896972185e-26 - 1.5605472050910189342e-1750j 2.07e-160, 3.7e-403j
3.3202285173649623982e-21 + 2.0910754171256068472e-1747j 1.05e-157, 1.87e-400j
0.010180486966820036042 + 6.9453519600756327532e-1734j 2.43e-130, 4.35e-373j
2.3407985775094274995e-06 + 2.2866981831812532816e-1737j 1.18e-143, 2.1e-386j
1.1165638046236163131e-24 + 1.6997542774648953459e-1748j 1.08e-160, 1.93e-403j
-0.012329250865960376594 - 1.7877410142564296831e-1732j 1.77e-127, 3.17e-370j
2.3735036306873136635e-15 + 8.6650336450610744424e-1744j 4.97e-154, 8.88e-397j
6.8332082082551728718e-23 - 2.1090974081502719268e-1748j 7.39e-159, 1.32e-401j
0.082820652211898959085 - 3.5008555706275922087e-1733j 4.22e-130, 7.54e-373j
9.4880219116676970845e-11 + 4.5543955832997597677e-1740j 3.11e-155, 5.55e-398j
0.021023446176933828063 - 1.6826911483930555176e-1733j 5.52e-134, 9.85e-377j
5.7129499401271374237e-09 + 1.7632523945590887273e-1738j 4.25e-153, 7.58e-396j
4.1425524721452930844e-18 + 1.5667612534906311953e-1745j 1.37e-156, 2.45e-399j
1.3921882455570943928e-28 + 1.1202296984038471412e-1751j 6.26e-163, 1.12e-405j
9.4880219116676970845e-11 + 1.5155851988541072219e-1740j 2.43e-153, 4.33e-396j
4.5777542453768194457e-05 + 3.0941902671206747638e-1736j 2.95e-150, 5.26e-393j
5.0277115770371718552e-38 + 6.289544892961363846e-1757j 3.03e-168, 5.4e-411j
2.3735036306873136635e-15 + 3.6213376240911368674e-1743j 4.52e-161, 8.08e-404j
1.1029189351314742533e-05 - 1.1810232671341429678e-1736j 4.86e-152, 8.68e-395j
3.3202285173649623982e-21 + 1.3508526196011905091e-1746j 2.57e-163, 4.59e-406j
4.3980736060521185694e-07 - 1.0181685580849052836e-1737j 4.78e-152, 8.55e-395j
0.0014137480586794681255 - 8.0507496062231417285e-1735j 3.7e-148, 6.61e-391j
0.068080405186430768737 + 1.6229647423486710099e-1732j 1.46e-141, 2.61e-384j
8.6587287071912553257e-12 - 7.8198022057212709492e-1741j 1.18e-158, 2.11e-401j
0.10357013340969829466 + 2.7769619212913911971e-1733j 1.64e-143, 2.93e-386j
0.021023446176933828063 - 1.2552294099201242143e-1733j 2.89e-144, 5.15e-387j
8.6010801868929104488e-10 - 9.8380119098806449295e-1740j 7.27e-155, 1.3e-397j
0.082820652211898959085 - 4.0436732202720175604e-1733j 2.36e-144, 4.21e-387j
0.00016663754356262415823 - 8.5934043518260850642e-1736j 1.34e-151, 2.39e-394j
0.002927442002278737574 + 1.6746670064047077064e-1734j 8.06e-148, 1.44e-390j
8.6587287071912553257e-12 - 2.4128980359368025901e-1741j 1.96e-156, 3.49e-399j
8.6010801868929104488e-10 - 2.7529042818126443887e-1739j 9.69e-158, 1.73e-400j
1.0878515547341322243e-16 - 5.5447031150407827702e-1744j 1.03e-162, 1.85e-405j
4.3346836662117232975e-14 - 2.2484187290481585112e-1742j 3.36e-161, 6e-404j
4.5777542453768194457e-05 + 1.6369035640026644901e-1736j 5.38e-154, 9.68e-397j
0.11716713091098831958 - 2.6691423116283174884e-1733j 1.66e-150, 3.01e-393j
-0.012329250865960376594 - 1.4510236562180597208e-1732j 3.92e-150, 7.05e-393j
1.636600697359080156e-08 - 6.9919343340399076563e-1738j 3.27e-157, 5.83e-400j
0.10357013340969829466 + 3.0539104976552581307e-1733j 1.56e-151, 2.89e-394j
2.3407985775094274995e-06 + 4.8679627310141668036e-1737j 1.61e-156, 2.86e-399j
0.068080405186430768737 + 1.3345719213965434835e-1732j 5.85e-151, 1.1e-393j
7.2301298005616728327e-08 + 5.6576917524995084122e-1738j 3.5e-157, 6.27e-400j
0.11716713091098831958 - 2.7979757745260865773e-1733j 2.18e-152, 4.19e-395j
0.00052753150867431308205 + 2.5387340279866851175e-1735j 8.07e-155, 1.38e-397j
0.12169010664828899796 + 2.7081953654165588153e-1733j 1.78e-152, 3.49e-395j

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.