Rule: Q[18, 19, 38]

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)
0.9997854595658100238 + 1.7522996486556715148e-846j 7.23e-228, 7.23e-228j
-0.95582394957139775518 - 1.8305658878966211977e-849j 2.07e-228, 2.07e-228j
-0.94249684146906849299 - 1.2307714175648352211e-853j 1.1e-228, 1.1e-228j
-0.9997854595658100238 - 8.0100643483192239336e-851j 7.21e-228, 7.21e-228j
0.94249684146906849299 - 1.9890912132095692913e-872j 1.13e-228, 1.13e-228j
0.92750450157334331639 + 5.6002757974358877849e-872j 4.67e-229, 4.67e-229j
0.99156516842093094673 + 3.7284738502106720042e-869j 1.46e-227, 1.46e-227j
-0.89260246649755573921 + 2.0095342398538178218e-874j 7.25e-230, 7.25e-230j
-0.91086875164380673424 - 8.0697350728875952503e-873j 2e-229, 2e-229j
-0.99859916541268279031 - 1.9459377271022852638e-876j 1.75e-227, 1.75e-227j
0.85124937343371764175 - 2.523455207320184559e-906j 6.63e-231, 6.63e-231j
-0.99594304344280852964 + 2.5391393122169659689e-900j 1.96e-227, 1.96e-227j
-0.92750450157334331639 + 3.6629451238687287562e-917j 5.1e-229, 5.1e-229j
-0.872720812627312149 + 2.0565412213092802363e-923j 2.3e-230, 2.3e-230j
0.98536049239177134719 + 3.2792225236440559014e-921j 1.02e-227, 1.02e-227j
0.872720812627312149 + 1.4051800429520198927e-926j 2.45e-230, 2.45e-230j
0.89260246649755573921 + 4.154461501561472825e-926j 7.3e-230, 7.3e-230j
0.97731038077486095188 + 2.405909816128665171e-922j 6.69e-228, 6.69e-228j
-0.77773803822426885768 - 2.7368720981031206766e-926j 9.82e-233, 9.82e-233j
-0.96744661827403191685 + 3.6767357205032235313e-927j 4.41e-228, 4.41e-228j
0.91086875164380673424 - 8.0417506996003214488e-939j 1.82e-229, 1.82e-229j
0.75038048170335763518 + 1.972926526690495665e-942j 2.13e-233, 2.13e-233j
-0.98536049239177134719 - 1.385658621299034408e-934j 1.07e-227, 1.07e-227j
-0.80370495897252311568 - 9.0807673821875007804e-950j 4.6e-232, 4.6e-232j
-0.75038048170335763518 + 7.9210663551123216464e-951j 2.11e-233, 2.11e-233j
0.99859916541268279031 - 2.4939688150774941743e-942j 1.73e-227, 1.73e-227j
0.77773803822426885768 + 4.8256671762740289521e-952j 1.14e-232, 1.14e-232j
0.80370495897252311568 - 5.8976084750465239203e-952j 5.28e-232, 5.28e-232j
-0.99156516842093094673 + 4.1574421451802077149e-944j 1.48e-227, 1.48e-227j
-0.66044394514363288709 - 1.047749643828020025e-959j 8.33e-236, 8.33e-236j
0.25188622569150550959 - 3.9445540247424338269e-971j 9.53e-248, 9.53e-248j
0.82822726453683750169 + 4.8293206755675426357e-953j 2.01e-231, 2.01e-231j
0.69168704306035320787 - 8.1191816577522002065e-957j 6.14e-235, 6.14e-235j
-0.97731038077486095188 - 2.3598044832153145715e-949j 6.71e-228, 6.71e-228j
-0.72168149710605615977 + 3.8021380182024076598e-961j 3.48e-234, 3.48e-234j
-0.69168704306035320787 - 6.0249018098415914556e-962j 5.89e-235, 5.89e-235j
0.99594304344280852964 + 1.0894629092506685618e-951j 1.84e-227, 1.84e-227j
0.59442465242386579359 - 2.486818509542929627e-965j 1.19e-237, 1.19e-237j
0.95582394957139775518 - 1.4762605558446599137e-954j 2.23e-228, 2.23e-228j
-0.85124937343371764175 - 4.9772978686671488195e-962j 7.33e-231, 7.33e-231j
-0.55977083107394753461 + 9.9359447552632690787e-970j 1.41e-238, 1.41e-238j
0.96744661827403191685 + 1.2807676333305847739e-965j 4.05e-228, 4.05e-228j
0.72168149710605615977 + 8.9153175834111927125e-974j 3.59e-234, 3.59e-234j
0.55977083107394753461 + 5.5044640229211572754e-978j 1.41e-238, 1.41e-238j
-0.16893682806654922601 - 2.0929382318627486533e-987j 2.26e-250, 2.26e-250j
-0.52410977624660693757 + 7.3691075173244000703e-976j 1.19e-239, 1.19e-239j
-0.82822726453683750169 + 2.4113085083801896853e-975j 1.97e-231, 1.97e-231j
0.66044394514363288709 + 2.4016174869722158364e-980j 8.63e-236, 8.63e-236j
0.45003454613950700326 + 4.3013700186322008057e-987j 9.53e-242, 9.53e-242j
0.6280037548638336526 - 5.4181454041212116237e-984j 1.09e-236, 1.09e-236j
-0.6280037548638336526 - 7.0170709315915898962e-982j 1.08e-236, 1.08e-236j
-0.48750904258507848736 + 1.4976434828943344836e-987j 1.08e-240, 1.08e-240j
-0.59442465242386579359 + 1.5055532698863600404e-990j 1.28e-237, 1.28e-237j
0.52410977624660693757 + 3.1480728750370207045e-994j 1.17e-239, 1.17e-239j
0.48750904258507848736 + 3.6513997653579726774e-996j 1.07e-240, 1.07e-240j
9.8741001473161647196e-1053 + 5.8005731482942409296e-1053j 8.59e-1051, 8.59e-1051j
-0.45003454613950700326 + 6.289171032493166116e-996j 9.71e-242, 9.71e-242j
-0.21060032237529332509 + 1.0793792056966191306e-1003j 4.75e-249, 4.75e-249j
0.12697028623003985378 + 7.3784476490889437321e-1009j 1.17e-251, 1.17e-251j
0.41175116146284264604 - 1.0328917336490382952e-999j 6.88e-243, 6.88e-243j
0.21060032237529332509 - 7.8399923763152916202e-1006j 4.88e-249, 4.88e-249j
-0.33302342279140787912 + 7.3521428822742969363e-1000j 3.07e-245, 3.07e-245j
-0.41175116146284264604 + 4.64164321063802178e-997j 7.02e-243, 7.02e-243j
-0.042426126620321295862 - 3.3109482000222529107e-1010j 2.31e-254, 2.31e-254j
0.37272465528630327839 + 2.1724597506056055048e-999j 4.57e-244, 4.57e-244j
0.29271914560631254443 + 9.0557794027446495446e-1002j 1.74e-246, 1.74e-246j
-0.084775013041735301242 + 2.0424143151223267975e-1008j 4.64e-253, 4.64e-253j
-0.37272465528630327839 - 1.7463126770079399449e-998j 4.64e-244, 4.64e-244j
-0.12697028623003985378 + 1.7063968382337626185e-1007j 1.05e-251, 1.05e-251j
0.16893682806654922601 + 7.0755109747496646741e-1007j 2.34e-250, 2.34e-250j
0.33302342279140787912 - 4.200188243283130597e-1001j 3.19e-245, 3.19e-245j
0.084775013041735301242 + 2.0960242580443995242e-1009j 5.03e-253, 5.03e-253j
-0.25188622569150550959 - 1.1206305060504982648e-1002j 1.04e-247, 1.04e-247j
-0.29271914560631254443 + 7.5867698036820162611e-1003j 1.87e-246, 1.87e-246j
0.042426126620321295862 + 3.0139081968920625618e-1013j 2.31e-254, 2.31e-254j

Weights

Weight (ball center) Error (ball radius)
0.00059431822719970361102 - 1.6027150252158266623e-846j 2.03e-17, 5.18e-124j
0.012482995131820978999 + 1.6654461461474711639e-849j 9.81e-18, 2.51e-124j
0.014164657266859529987 + 1.5784875682757572612e-850j 8.86e-18, 2.26e-124j
0.00059431822719970361102 - 7.732652349262593803e-850j 7.63e-19, 1.95e-125j
0.014164657266859529987 - 5.305904207819819486e-848j 2.84e-19, 7.26e-126j
0.015816548945421744753 + 4.237080876377142149e-848j 2.32e-19, 5.93e-126j
0.0052824165178332483514 + 3.9241509790044582721e-847j 1.07e-19, 2.74e-126j
0.019077173591497796721 + 1.2615636547140801887e-849j 6.35e-20, 1.62e-126j
0.017453007112248788053 - 1.0949820981156788333e-849j 1e-19, 2.57e-126j
0.0018623128264572330998 + 1.8416940503413167678e-849j 2.97e-20, 7.59e-127j
0.022254397701202670196 + 2.0662177868138363821e-848j 6.5e-24, 1.66e-130j
0.003489920064401463041 - 2.2173363060489399403e-849j 1.16e-20, 2.96e-127j
0.015816548945421744753 + 7.7333183168001599321e-850j 1.06e-20, 2.7e-127j
0.020681923070436301221 - 1.3649186897014974283e-849j 2.83e-22, 7.22e-129j
0.0071294770620409827141 - 2.1792760071591633354e-847j 1.24e-23, 3.16e-130j
0.020681923070436301221 - 2.4214088987630704613e-848j 3.59e-24, 9.17e-131j
0.019077173591497796721 + 2.8749485828253115397e-848j 2.89e-24, 7.38e-131j
0.0089650006105371810505 + 1.3627138367446338325e-847j 1.33e-24, 3.39e-131j
0.026670858898539554601 - 1.5959614976508834876e-849j 3.13e-26, 8.01e-133j
0.010752999903154295799 - 3.5081842596056127197e-849j 4.9e-23, 1.25e-129j
0.017453007112248788053 - 3.4613015365465768172e-848j 2.83e-24, 7.23e-131j
0.02803608460530603592 + 1.2302090304412268238e-848j 4.34e-28, 1.11e-134j
0.0071294770620409827141 - 2.3986664470180174735e-849j 1.92e-23, 4.92e-130j
0.025253930307278584375 + 1.5475600111531796277e-849j 2.01e-26, 5.13e-133j
0.02803608460530603592 + 1.6425029730042478605e-849j 1.59e-27, 4.07e-134j
0.0018623128264572330998 + 2.1689788106089314233e-846j 1.06e-25, 2.7e-132j
0.026670858898539554601 - 1.3800394795247503451e-848j 8.98e-29, 2.3e-135j
0.025253930307278584375 + 1.5615786638179355864e-848j 1.8e-28, 4.59e-135j
0.0052824165178332483514 + 2.3205473716500276817e-849j 1.02e-24, 2.61e-131j
0.031850765975176333629 - 1.7737646122854701084e-849j 8.34e-32, 2.13e-138j
0.041072040403555827203 + 4.0894257327485229126e-849j 2.43e-35, 6.2e-142j
0.023781294166088060127 - 1.7856073981525909087e-848j 2.62e-28, 6.7e-135j
0.030626870883583499374 + 9.9696562201785816104e-849j 6.93e-32, 1.77e-138j
0.0089650006105371810505 + 2.6337017361617758033e-849j 1.55e-25, 3.97e-132j
0.029354301069229018794 - 1.6873907265953380387e-849j 4.58e-31, 1.17e-137j
0.030626870883583499374 + 1.7308875784983906741e-849j 8.19e-32, 2.09e-138j
0.003489920064401463041 - 8.2261186772395931302e-847j 1.51e-28, 3.86e-135j
0.034127549626105226479 - 7.5616326068245291178e-849j 2.69e-36, 6.89e-143j
0.012482995131820978999 + 6.8706813643517965492e-848j 8.16e-30, 2.09e-136j
0.022254397701202670196 + 1.4378939764594668768e-849j 3.42e-31, 8.75e-138j
0.035168786118204499148 + 1.9107206229250278502e-849j 1.72e-37, 4.4e-144j
0.010752999903154295799 - 9.3464989277050756366e-848j 1.01e-29, 2.57e-136j
0.029354301069229018794 - 1.1042902797877853001e-848j 4.68e-34, 1.2e-140j
0.035168786118204499148 + 6.963710317237428205e-849j 4.86e-38, 1.24e-144j
0.041827387121796914532 + 2.6003723595749361435e-849j 1.92e-42, 4.92e-149j
0.036142033811172968913 - 1.9621483763426526399e-849j 2.26e-39, 5.77e-146j
0.023781294166088060127 - 1.4960985442389182655e-849j 2.54e-33, 6.5e-140j
0.031850765975176333629 - 9.0470311034426910931e-849j 9.45e-37, 2.42e-143j
0.037889756523076807477 - 5.5754261185106077164e-849j 2.28e-41, 5.83e-148j
0.033019906902409527049 + 8.2506254621981293743e-849j 8.24e-38, 2.11e-144j
0.033019906902409527049 + 1.8172282594389508618e-849j 4.71e-38, 1.2e-144j
0.037048460419476432528 + 2.0168360707146020958e-849j 1.69e-41, 4.31e-148j
0.034127549626105226479 - 1.8625593094207000803e-849j 7.76e-39, 1.98e-145j
0.036142033811172968913 - 6.4418745866872378353e-849j 6.96e-41, 1.78e-147j
0.037048460419476432528 + 5.9827779662841846264e-849j 9.9e-42, 2.53e-148j
0.042439032170324879187 + 3.0500471155125464542e-849j 1.4e-47, 3.58e-154j
0.037889756523076807477 - 2.0746414591070674446e-849j 6.17e-44, 1.58e-150j
0.041487190310326946412 - 2.5078948579551088717e-849j 9.15e-47, 2.34e-153j
0.042093330485895000625 - 3.5002331013825828021e-849j 1.17e-47, 2.98e-154j
0.038666082667878870011 + 5.2115017245327468098e-849j 4.23e-45, 1.08e-151j
0.041487190310326946412 - 3.8741501296199206477e-849j 3.11e-47, 7.95e-154j
0.040014966315597486636 + 2.2688634001251695598e-849j 1.21e-47, 3.11e-154j
0.038666082667878870011 + 2.1356086406384841218e-849j 2.19e-46, 5.59e-153j
0.042400332119658527806 - 2.9238298834278159416e-849j 5.91e-49, 1.51e-155j
0.039375541627478758383 - 4.8850170175387448667e-849j 2.8e-47, 7.15e-154j
0.040581161255325955013 - 4.3274730009547870086e-849j 4.78e-48, 1.22e-154j
0.042284704270564807774 + 2.807527693490611009e-849j 1.16e-49, 2.96e-156j
0.039375541627478758383 - 2.2001233529863458268e-849j 6.64e-49, 1.7e-155j
0.042093330485895000625 - 2.70002190229262782e-849j 9.12e-50, 2.33e-156j
0.041827387121796914532 + 3.6786121518775401415e-849j 4.12e-50, 1.05e-156j
0.040014966315597486636 + 4.5915506481169757029e-849j 1.84e-49, 4.72e-156j
0.042284704270564807774 + 3.3370000420926909705e-849j 6.86e-51, 1.77e-157j
0.041072040403555827203 + 2.4221184834744018092e-849j 1.75e-51, 4.59e-158j
0.040581161255325955013 - 2.342622318025601134e-849j 1.73e-51, 4.6e-158j
0.042400332119658527806 - 3.1873677485075677676e-849j 1.66e-51, 4.05e-158j

Download

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