Rule: Q[1, 2, 8, 24, 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)
-0.99750388282687745465 + 1.4293862806740476556e-842j 1.74e-229, 1.74e-229j
-0.95426326163001177301 + 1.5587501280512650896e-850j 2.33e-230, 2.33e-230j
-0.9225217132136291628 + 1.5407431113059700688e-854j 2.72e-231, 2.72e-231j
-0.99968994604588528675 - 3.4396916106258716463e-853j 4.97e-230, 4.97e-230j
0.9225217132136291628 - 4.8670449548471365028e-874j 2.6e-231, 2.6e-231j
0.93958627662515351534 + 3.9657049421900266909e-873j 8.02e-231, 8.02e-231j
0.99750388282687745465 + 1.4250150670048381486e-870j 1.65e-229, 1.65e-229j
-0.93958627662515351534 + 7.8710883021075764791e-870j 8.36e-231, 8.36e-231j
-0.98585717925374526599 - 2.592980371363448522e-883j 3.68e-229, 3.68e-229j
0.99968994604588528675 + 3.2633289764612471256e-896j 5.5e-230, 5.5e-230j
0.90323324705211838243 + 7.651868194030757937e-899j 7.95e-232, 7.95e-232j
0.99079325588510780584 + 4.3065480821358228182e-894j 1.1e-228, 1.1e-228j
-0.88175702448602086613 + 5.999494547075989906e-898j 2.01e-232, 2.01e-232j
-0.90323324705211838243 + 4.5180005477851886607e-901j 7.21e-232, 7.21e-232j
0.63680349166384192103 + 7.2926142036523849674e-921j 1.36e-238, 1.36e-238j
0.88175702448602086613 - 7.1058242069756964378e-914j 2.02e-232, 2.02e-232j
0.85809426417506453171 + 9.6408239667733031653e-914j 4.73e-233, 4.73e-233j
-0.99079325588510780584 - 2.6351884483610442104e-906j 1.02e-228, 1.02e-228j
-0.80443977651116548294 + 6.3629734461393812041e-927j 2.26e-234, 2.26e-234j
-0.96651154934785648947 + 2.8157112878240959695e-920j 5.67e-230, 5.67e-230j
0.96651154934785648947 + 5.9763841068783191943e-936j 5.74e-230, 5.74e-230j
0.74283095577941597325 - 5.1416601106626849875e-945j 6.17e-236, 6.17e-236j
-0.97688244065119801513 - 7.2795899086138354913e-935j 1.24e-229, 1.24e-229j
-0.85809426417506453171 + 1.1556335501414348161e-946j 5.08e-233, 5.08e-233j
-0.77459666924148337704 - 1.1385764269201673109e-948j 3.77e-235, 3.77e-235j
0.99258491546402838393 + 5.6025136976672222871e-940j 9.36e-229, 9.36e-229j
0.77459666924148337704 + 7.1611947779987841329e-950j 3.83e-235, 3.83e-235j
0.95426326163001177301 - 4.4063815501618854472e-943j 2.18e-230, 2.18e-230j
-0.99258491546402838393 + 3.9158789795109242521e-943j 8.93e-229, 8.93e-229j
-0.63680349166384192103 + 3.7653380118209682687e-961j 1.36e-238, 1.36e-238j
-0.1962927094566443174 - 5.5860622842303058108e-974j 2.42e-250, 2.42e-250j
0.83229562803130494137 - 6.3505148491806623977e-955j 1.09e-233, 1.09e-233j
0.67384653116795819852 - 2.2629526320837858687e-959j 1.19e-237, 1.19e-237j
0.97688244065119801513 + 2.423967233595159838e-949j 1.26e-229, 1.26e-229j
-0.67384653116795819852 - 1.4937999128971928942e-963j 1.15e-237, 1.15e-237j
-0.70921858718567648513 + 2.809396538441501131e-962j 8.99e-237, 8.99e-237j
0.98585717925374526599 - 2.4686086404835046218e-961j 3.71e-229, 3.71e-229j
0.59817869459985908152 + 4.9222207534064002797e-975j 1.41e-239, 1.41e-239j
0.80443977651116548294 + 9.1571519430213204153e-970j 2.23e-234, 2.23e-234j
-0.74283095577941597325 - 7.1221669638886306951e-970j 6.41e-236, 6.41e-236j
-0.14764774508719404062 + 9.6462592553529505745e-987j 1.05e-251, 1.05e-251j
-0.83229562803130494137 + 5.9451905990541984583e-975j 1.13e-233, 1.13e-233j
0.70921858718567648513 + 1.8571365170132961643e-983j 8.89e-237, 8.89e-237j
0.55806685067819680295 + 4.1978636552217050611e-987j 1.34e-240, 1.34e-240j
0.049379708371318616538 + 6.7201558282436849082e-1001j 2.45e-254, 2.45e-254j
-0.55806685067819680295 + 4.5231353700247844508e-985j 1.27e-240, 1.27e-240j
-0.59817869459985908152 - 6.3088546547511257891e-988j 1.4e-239, 1.4e-239j
0.098636293502968334058 + 2.1733962489037636175e-1002j 4.68e-253, 4.68e-253j
0.47378868408257621959 - 1.975410100831197114e-990j 8.55e-243, 8.55e-243j
0.33882276544933496447 + 1.0288254823140767527e-994j 1.97e-246, 1.97e-246j
-0.38480501431708872328 + 4.2227371707189017471e-993j 3.69e-245, 3.69e-245j
-0.33882276544933496447 - 2.6990623798938098536e-994j 1.98e-246, 1.98e-246j
-0.098636293502968334058 + 1.1887982577403913646e-1001j 4.68e-253, 4.68e-253j
0.42983118675332573891 + 6.6985488042016987316e-992j 5.51e-244, 5.51e-244j
0.51656894978121625306 + 1.8662598029894369905e-990j 1.18e-241, 1.18e-241j
4.1228297778817391273e-1042 - 2.340430739604279615e-1042j 3.18e-1040, 3.18e-1040j
-0.47378868408257621959 + 4.508272736110413535e-990j 8.76e-243, 8.76e-243j
-0.2444499006003230238 + 6.3197588215267726534e-998j 4.6e-249, 4.6e-249j
0.14764774508719404062 - 1.8744186895472435164e-1001j 1.1e-251, 1.1e-251j
0.38480501431708872328 - 2.2639850006943083246e-994j 3.6e-245, 3.6e-245j
0.1962927094566443174 + 6.6310861029533592565e-999j 2.43e-250, 2.43e-250j
-0.2919991541426287378 - 4.5183446552872266076e-997j 1.1e-247, 1.1e-247j
-0.42983118675332573891 - 1.3331635374221764163e-991j 6.03e-244, 6.03e-244j
-0.049379708371318616538 - 5.6368579740049813544e-1003j 2.49e-254, 2.49e-254j
0.2919991541426287378 + 1.1997089936139034949e-997j 1.04e-247, 1.04e-247j
0.2444499006003230238 + 1.0007370866935445751e-998j 4.76e-249, 4.76e-249j
-0.51656894978121625306 - 9.7261544493375005372e-990j 1.21e-241, 1.21e-241j

Weights

Weight (ball center) Error (ball radius)
0.0034926342640348571194 + 1.064794768703402986e-842j 1.53e-31, 1.52e-138j
0.01342781709147694178 + 1.1888023866987014609e-843j 5.78e-32, 5.78e-139j
0.018192774893979594766 + 3.6137876799408328215e-844j 3.28e-32, 3.28e-139j
0.00097399109776847427602 + 6.1059104201177210169e-843j 4.3e-32, 4.29e-139j
0.018192774893979594766 + 1.4112813212153846973e-845j 1.23e-33, 1.23e-140j
0.015905693813070945751 - 1.9017350432927052631e-845j 1.05e-33, 1.05e-140j
0.0034926342640348571194 + 2.5024081581679516599e-845j 7.73e-35, 7.72e-142j
0.015905693813070945751 - 6.3604712248141183901e-844j 9.49e-33, 9.48e-140j
0.0082741861072400821972 - 1.6232075587665753735e-842j 6.75e-33, 6.74e-140j
0.00097399109776847427602 - 6.6833306440195445812e-846j 5.01e-35, 5e-142j
0.020380673987280225253 - 1.0831885368044824704e-845j 1.2e-35, 1.2e-142j
-0.0012019428130744494694 + 2.1682391737254598071e-844j 2.55e-35, 2.55e-142j
0.022573154840132166085 + 1.3831044806054768665e-844j 2.69e-35, 2.69e-142j
0.020380673987280225253 - 2.1839852068539651474e-844j 1.4e-34, 1.4e-141j
0.037849097630040105783 + 2.4645738379431418477e-846j 9.38e-39, 9.37e-146j
0.022573154840132166085 + 8.5187742706439069809e-846j 7.06e-37, 7.06e-144j
0.024743225310660879633 - 6.8416784608729456518e-846j 1.6e-37, 1.59e-144j
-0.0012019428130744494694 + 6.4242932453366569971e-842j 2.39e-35, 2.39e-142j
0.028860021953494589175 - 4.385703587046803551e-845j 8.8e-40, 8.79e-147j
0.011175347993946907847 - 2.2695891302011104761e-843j 3.99e-36, 3.99e-143j
0.011175347993946907847 - 3.5814318058909984027e-845j 3.7e-40, 3.69e-147j
0.032702940996225311215 - 3.4694495457607861997e-846j 1.92e-42, 1.92e-149j
0.0096618948855970192226 + 4.6433975366240687532e-843j 4.57e-36, 4.57e-143j
0.024743225310660879633 - 9.1065496178723665851e-845j 1.75e-39, 1.75e-146j
0.030815784385771608725 + 3.1838654410456425896e-845j 1e-41, 1e-148j
0.0068561201200961336357 - 1.6787549806160932479e-844j 1.3e-39, 1.3e-146j
0.030815784385771608725 + 4.0048888130568257156e-846j 1.43e-43, 1.43e-150j
0.01342781709147694178 + 2.6337444421456919927e-845j 1.28e-40, 1.27e-147j
0.0068561201200961336357 - 6.7918143768411303429e-842j 8.36e-37, 8.34e-144j
0.037849097630040105783 + 1.1166805789231407052e-845j 2.41e-46, 2.41e-153j
0.048421259777417164816 + 2.4989082831865624005e-846j 7.27e-49, 7.26e-156j
0.026840187527539801777 + 5.6130204231356883222e-846j 3.39e-43, 3.38e-150j
0.036222228031879538689 - 2.7243179969639562634e-846j 5.83e-46, 5.82e-153j
0.0096618948855970192226 + 4.8497885243536413063e-845j 3.36e-41, 3.35e-148j
0.036222228031879538689 - 1.406824227046683416e-845j 2.53e-47, 2.53e-154j
0.03450709208415847981 + 1.8069878212800828909e-845j 6.23e-47, 6.22e-154j
0.0082741861072400821972 - 9.5318087599173672667e-845j 5.39e-41, 5.39e-148j
0.039384722129652090601 - 2.2578978722884030488e-846j 3.9e-49, 3.9e-156j
0.028860021953494589175 - 4.6989367847511450631e-846j 5.83e-45, 5.83e-152j
0.032702940996225311215 - 2.3708856804347085201e-845j 4.77e-47, 4.76e-154j
0.048848432435282704285 - 2.2971250014938731607e-846j 8.23e-54, 8.22e-161j
0.026840187527539801777 + 6.2168214146561868662e-845j 1.19e-45, 1.19e-152j
0.03450709208415847981 + 3.0522127893521437428e-846j 1.65e-47, 1.65e-154j
0.040822051209166797906 + 2.0936034010289779712e-846j 7.23e-51, 7.22e-158j
0.049338586528789135133 - 1.812019760950101623e-846j 2.04e-55, 2.04e-162j
0.040822051209166797906 + 7.411182833110634394e-846j 9.29e-53, 9.28e-160j
0.039384722129652090601 - 9.0224419004240491096e-846j 1.06e-51, 1.06e-158j
0.049154261305064007301 + 1.7493044160550281784e-846j 2.23e-56, 2.23e-163j
0.043386612497735799091 + 1.8623668989659724852e-846j 7.35e-55, 7.34e-162j
0.046422124952888737898 - 1.6907491639873841898e-846j 1.48e-56, 1.47e-163j
0.04552323142681988366 + 3.8997398275482338374e-846j 7.94e-57, 7.93e-164j
0.046422124952888737898 - 3.4301775277411593203e-846j 4.37e-57, 4.37e-164j
0.049154261305064007301 + 2.133220592869499685e-846j 1.18e-57, 1.18e-164j
0.044510302838450992184 - 1.7849968344911883932e-846j 7.18e-57, 7.17e-164j
0.042156446068599199448 - 1.9637651175582530693e-846j 1.49e-55, 1.49e-162j
0.049400285555576374805 + 1.8949177875173624792e-846j 1.05e-58, 1.05e-165j
0.043386612497735799091 + 5.2320165397953023329e-846j 2.82e-58, 2.82e-165j
0.047873065258468821267 - 2.7470257843478771902e-846j 1.38e-58, 1.37e-165j
0.048848432435282704285 - 1.7047749249489626219e-846j 1.37e-59, 1.37e-166j
0.04552323142681988366 + 1.7285327328141953942e-846j 6.27e-59, 6.26e-166j
0.048421259777417164816 + 1.6771309694385638231e-846j 3.72e-60, 3.71e-167j
0.047205836592557265738 + 3.052549316108187402e-846j 6.8e-60, 6.77e-167j
0.044510302838450992184 - 4.488129522339811135e-846j 4.19e-60, 4.18e-167j
0.049338586528789135133 - 2.0007650961101104302e-846j 3.07e-60, 3.08e-167j
0.047205836592557265738 + 1.6700914326136769466e-846j 4.24e-61, 4.24e-168j
0.047873065258468821267 - 1.6656486994064939085e-846j 3.73e-61, 3.75e-168j
0.042156446068599199448 - 6.1822987232266244793e-846j 3.63e-61, 3.32e-168j

Download

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