Rule: Q[4, 36]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ 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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{40}-\frac{99442554902096924593335}{2322703455426597460151}\cdot t^{38}+\frac{21538780564496573187125218383}{111229623073468899171711088}\cdot t^{36}-\frac{2120534429171687103569224608105}{3948651619108145920595743624}\cdot t^{34}+\frac{16868444888432463587420835479895}{16512543134452246577036746064}\cdot t^{32}-\frac{97681423926441879382690525306977}{69146274375518782541341374143}\cdot t^{30}+\frac{406193457982009545788326617295155}{276585097502075130165365496572}\cdot t^{28}-\frac{161896809230037335577795135483537}{138292548751037565082682748286}\cdot t^{26}+\frac{3051286182836152403591966331894300}{4217922736906645735021823822723}\cdot t^{24}-\frac{342343134167101406311761190155975}{983626250899178254412203974469}\cdot t^{22}+\frac{1024765794654711681153632508143595}{7869010007193426035297631795752}\cdot t^{20}-\frac{26720679482982857257074416743425}{709500902287931855641589752076}\cdot t^{18}+\frac{419868071499793997769225049975410585}{50463961176131441164363712706157576}\cdot t^{16}-\frac{129834093040067287612309947003675}{94149181298752688739484538630891}\cdot t^{14}+\frac{4214550074198823318064594104828225}{25231980588065720582181856353078788}\cdot t^{12}-\frac{5371631691689313417618203119360245}{377332800612437366888083215461950966}\cdot t^{10}+\frac{1218953262828200686536142298596275}{1509331202449749467552332861847803864}\cdot t^8-\frac{32447898402564857579923014498780}{1158950744738200484013398447490277967}\cdot t^6+\frac{390483831960526183509126024677175}{760271688548259517512789381553622346352}\cdot t^4-\frac{1423305454099564209301911420975}{380135844274129758756394690776811173176}\cdot t^2+\frac{314194402584060284061625815}{69115608049841774319344489232147486032}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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