Rule: Q[16, 17]

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.

• $P_1$:
  $\frac{300540195}{32768}\cdot t^{16}-\frac{145422675}{4096}\cdot t^{14}+\frac{456326325}{8192}\cdot t^{12}-\frac{185910725}{4096}\cdot t^{10}+\frac{334639305}{16384}\cdot t^8-\frac{20369349}{4096}\cdot t^6+\frac{4849845}{8192}\cdot t^4-\frac{109395}{4096}\cdot t^2+\frac{6435}{32768}$
• $P_2$:
  $\frac{300540195}{32768}\cdot t^{33}-\frac{17340199767}{229376}\cdot t^{31}+\frac{21032700321303}{74260480}\cdot t^{29}-\frac{21565531690857517}{33788518400}\cdot t^{27}+\frac{865373180206080019221}{897000692224000}\cdot t^{25}-\frac{697066033781193252316767}{674993020898560000}\cdot t^{23}+\frac{36620438653994511812036602149}{45454030027309030400000}\cdot t^{21}-\frac{34722306309656950102410964173909}{74771879394923355008000000}\cdot t^{19}+\frac{1574815565353419839366476030258034643}{7940025872946911068299520000000}\cdot t^{17}-\frac{198128252898142727955007959272634129}{3176010349178764427319808000000}\cdot t^{15}+\frac{124130412218272309138880815238757}{8725303157084517657472000000}\cdot t^{13}-\frac{9993078415965191680269364583421}{4362651578542258828736000000}\cdot t^{11}+\frac{1089515784814320598932302780697}{4362651578542258828736000000}\cdot t^9-\frac{1076557527185041398425942710917}{62323593979175126124800000000}\cdot t^7+\frac{29719863741748102159663039581}{43626515785422588287360000000}\cdot t^5-\frac{1924541201681000052834647007}{152692805248979059005760000000}\cdot t^3+\frac{84828922796733979312295451}{1221542441991832472046080000000}\cdot t$

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.