Rule: Q[4, 8, 9, 32]

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)
0.99448488266736190842 - 1.6976732855599839877e-918j 1.35e-237, 1.35e-237j
0.99900152771046987452 + 4.7880319795194123936e-935j 4.94e-238, 4.94e-238j
-0.91887309143310793072 + 4.9172889785314591009e-945j 6.73e-238, 6.73e-238j
-0.98586118743525271537 - 4.9554771018203007519e-946j 2.12e-237, 2.12e-237j
0.91887309143310793072 - 4.0168889241009208938e-945j 6.85e-238, 6.85e-238j
0.86113631159405257522 - 2.8159619208639025793e-951j 8.55e-239, 8.55e-239j
0.9397547494236062695 - 1.9339806986446347423e-954j 1.49e-237, 1.49e-237j
-0.9397547494236062695 - 5.076712561927387712e-961j 1.4e-237, 1.4e-237j
-0.99900152771046987452 + 2.0813407026354297877e-960j 4.96e-238, 4.96e-238j
-0.95745039100336941747 - 1.4420495131716539012e-961j 1.81e-237, 1.81e-237j
0.78641193364718379371 + 1.8260636199918063031e-965j 7.28e-240, 7.28e-240j
0.18035397587349104032 + 5.8103010467925824524e-986j 6.73e-252, 6.73e-252j
-0.44049436796746310788 - 5.1528361641204307359e-980j 1.34e-245, 1.34e-245j
-0.78641193364718379371 + 3.703794688870439018e-974j 7.34e-240, 7.34e-240j
0.98586118743525271537 - 1.266692384101979486e-969j 1.92e-237, 1.92e-237j
0.82532282372445844191 - 9.7196468880104510297e-984j 2.61e-239, 2.61e-239j
-0.99448488266736190842 - 5.5666286713185421715e-980j 1.43e-237, 1.43e-237j
-0.9732162594524303742 - 1.6214476871289625599e-983j 2.12e-237, 2.12e-237j
-0.74669472955378212303 - 1.2715236265488063114e-986j 2.21e-240, 2.21e-240j
0.10993592177174489421 + 1.1955325883781498883e-998j 1.91e-253, 1.91e-253j
0.89262482951129479685 - 1.1594471706918908917e-981j 2.65e-238, 2.65e-238j
0.70849403391804515364 + 5.052897324468217264e-991j 6.4e-241, 6.4e-241j
0.9732162594524303742 + 1.7404898119096382566e-996j 2.13e-237, 2.13e-237j
-0.82532282372445844191 + 2.2567778291229414627e-1020j 2.66e-239, 2.66e-239j
-0.70849403391804515364 - 3.3462512005189230475e-1022j 6.71e-241, 6.71e-241j
0.35179811895933906019 + 8.9304780701829255898e-1021j 6.66e-245, 6.66e-245j
0.95745039100336941747 - 5.5127594024702992384e-1019j 1.94e-237, 1.94e-237j
0.74669472955378212303 + 1.8219915779377708013e-1032j 2.33e-240, 2.33e-240j
-0.89262482951129479685 + 8.2708700155235110564e-1035j 2.48e-238, 2.48e-238j
-0.61906704064062728044 + 4.9378454551291762889e-1041j 2.13e-242, 2.13e-242j
-0.86113631159405257522 - 8.4712690536712498865e-1043j 8.96e-239, 8.96e-239j
0.6674742407002819824 - 5.075078625916736137e-1046j 1.37e-241, 1.37e-241j
0.61906704064062728044 - 1.0303925093574104208e-1050j 2.05e-242, 2.05e-242j
-0.042042251717180302362 - 4.076609053993375653e-1059j 9.99e-255, 9.99e-255j
-0.6674742407002819824 - 4.5110965679070389435e-1051j 1.39e-241, 1.39e-241j
-0.50113917197545858012 + 2.6676399348110091111e-1054j 5.98e-244, 5.98e-244j
8.6027889223005433668e-1063 + 1.2004710328254363146e-1062j 7.83e-1061, 7.83e-1061j
0.56506095456170612105 - 8.136832070726473765e-1052j 3.68e-243, 3.68e-243j
0.35241611849142175407 - 1.8525424482974129108e-1054j 6.99e-245, 6.99e-245j
-0.18035397587349104032 + 1.6170160245681725586e-1062j 6.44e-252, 6.44e-252j
-0.56506095456170612105 - 1.9246074353097238221e-1052j 3.86e-243, 3.86e-243j
-0.25135692830352172779 - 5.9922067234781263837e-1060j 4.02e-250, 4.02e-250j
0.44049436796746310788 - 8.8160442020044285452e-1055j 1.35e-245, 1.35e-245j
0.50113917197545858012 - 3.1238826416148590989e-1052j 5.58e-244, 5.58e-244j
0.042042251717180302362 - 1.7860222117865496805e-1066j 9.99e-255, 9.99e-255j
-0.52029226136447175936 + 1.9348871329700069429e-1053j 1.49e-243, 1.49e-243j
-0.35179811895933906019 + 4.2859656954833615366e-1052j 6.43e-245, 6.43e-245j
0.25135692830352172779 - 3.1165022287097299272e-1062j 4.27e-250, 4.27e-250j
0.52029226136447175936 + 4.6412110792555627962e-1057j 1.44e-243, 1.44e-243j
0.3399810435848562648 - 4.0744864757049157052e-1060j 1.74e-246, 1.74e-246j
-0.3399810435848562648 - 9.8051936519407645148e-1057j 1.82e-246, 1.82e-246j
-0.35241611849142175407 - 2.0462055422225983223e-1061j 6.65e-245, 6.65e-245j
-0.10993592177174489421 + 6.6457812614769547333e-1069j 1.91e-253, 1.91e-253j

Weights

Weight (ball center) Error (ball radius)
0.0065256277214759653856 + 8.4848752024661689661e-919j 1.49e-58, 2.49e-172j
0.0026000101858839949002 + 7.3232772599234026699e-919j 1.16e-58, 1.94e-172j
0.023414647804905185759 - 5.4876552106769445844e-920j 7.48e-60, 1.25e-173j
0.010709959550841997509 - 1.1053871564490017344e-920j 1.53e-60, 2.56e-174j
0.023414647804905185759 - 1.3886523100521442412e-918j 9.85e-60, 1.65e-173j
0.033814882649451312507 - 9.5898131922507286232e-919j 2.49e-60, 4.18e-174j
0.018795535506325452825 + 1.6770590170839090798e-918j 6.37e-60, 1.07e-173j
0.018795535506325452825 + 4.7453098333747453004e-920j 3.49e-60, 5.84e-174j
0.0026000101858839949002 - 1.6592359879227472555e-921j 2.46e-61, 4.12e-175j
0.016833536030523521453 - 3.3309358875111759343e-920j 1.12e-60, 1.87e-174j
0.039829464208695981722 - 1.2772616938636366735e-918j 1.1e-61, 1.85e-175j
0.070650194052963739288 + 1.5153531477289202275e-918j 1.92e-63, 3.21e-177j
0.065507969478850829429 - 2.4093182705169562831e-918j 1.33e-63, 2.23e-177j
0.039829464208695981722 - 1.492302108005875048e-919j 2.22e-63, 3.72e-177j
0.010709959550841997509 - 2.5384119594869826044e-918j 1.07e-61, 1.8e-175j
0.037622054280098588776 + 1.0089099655266974842e-918j 3.14e-62, 5.26e-176j
0.0065256277214759653856 + 5.5699106378296469009e-921j 1.6e-61, 2.68e-175j
0.014431450401357469938 + 1.9715725938584016855e-920j 1.72e-61, 2.87e-175j
0.039030932858668295449 + 2.5813029124795973839e-919j 1.9e-64, 3.18e-178j
0.06999197679181632077 - 1.5804292381371770495e-918j 1.33e-65, 2.22e-179j
0.029007397770305104619 + 1.0904376858063928999e-918j 8.75e-63, 1.46e-176j
0.038254005425592990363 - 2.3534573487525328361e-918j 3.52e-65, 5.89e-179j
0.014431450401357469938 + 1.8240323341586578193e-918j 3.53e-63, 5.91e-177j
0.037622054280098588776 + 9.3784242399379822005e-920j 1.88e-65, 3.15e-179j
0.038254005425592990363 - 3.952293584553595106e-919j 2.52e-66, 4.22e-180j
-11.737464576205429594 - 2.3392727199685738576e-915j 1.08e-68, 1.81e-182j
0.016833536030523521453 - 1.7555988920161854971e-918j 1.47e-63, 2.46e-177j
0.039030932858668295449 + 1.8138380188644468578e-918j 6.45e-66, 1.08e-179j
0.029007397770305104619 + 5.8858284668243263983e-920j 1.22e-65, 2.04e-179j
0.051699639311212766442 - 7.1324706147025974867e-919j 7.08e-69, 1.18e-182j
0.033814882649451312507 - 6.8914274637588228175e-920j 5.14e-66, 8.61e-180j
0.044682921544455894538 + 2.6051092132475785259e-918j 4.72e-68, 7.9e-182j
0.051699639311212766442 - 3.0655473421722799754e-918j 5.37e-69, 8.99e-183j
0.062967011060937612533 + 2.6120478139340382036e-918j 2.43e-72, 4.07e-186j
0.044682921544455894538 + 5.1258687668095898006e-919j 1.63e-69, 2.72e-183j
0.050428572067410162826 + 5.2227950032296288354e-918j 1.39e-71, 2.33e-185j
0.024186421026358029756 - 3.8237536431367425879e-918j 2.07e-72, 3.46e-186j
0.055633897022818033852 + 5.7695833481517278206e-918j 1.08e-71, 1.8e-185j
11.226475870017963154 + 2.2319026760455641796e-915j 7.75e-71, 1.3e-184j
0.070650194052963739288 + 1.0500979119857676975e-918j 4.02e-74, 6.72e-188j
0.055633897022818033852 + 1.5886658062570198295e-918j 1.54e-72, 2.57e-186j
0.071804717102555495294 - 1.3969003528383344344e-918j 1.88e-74, 3.14e-188j
0.065507969478850829429 - 6.2407597867268071307e-918j 5.36e-74, 8.96e-188j
0.050428572067410162826 + 1.5833395669627655308e-917j 6.24e-74, 1.05e-187j
0.062967011060937612533 + 2.8426472602884494849e-918j 3.8e-74, 6.36e-188j
0.01408377012509300991 - 5.1832118637534199725e-918j 1.31e-73, 2.19e-187j
-11.737464576205429594 - 1.1167188562958152805e-915j 1.5e-75, 2.51e-189j
0.071804717102555495294 - 2.3418804999951686367e-918j 5.89e-76, 9.86e-190j
0.01408377012509300991 - 1.6557429430925794605e-917j 3.81e-75, 6.38e-189j
0.63057532272204769847 + 1.1182656516977972436e-916j 1.8e-74, 3.02e-188j
0.63057532272204769847 + 5.4846598009874948552e-917j 5.95e-77, 9.96e-191j
11.226475870017963154 + 1.0639497570620717527e-915j 1.16e-75, 1.94e-189j
0.06999197679181632077 - 1.2657920194406929385e-918j 1.21e-78, 2.02e-192j

Download

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