Rule: Q[49]

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.

• $P_1$:
  $\frac{3184701532372607112841303575}{70368744177664}\cdot t^{49}-\frac{4826300260399724181316202325}{8796093022208}\cdot t^{47}+\frac{54918216647285282526345418035}{17592186044416}\cdot t^{45}-\frac{97435545664538404482225741675}{8796093022208}\cdot t^{43}+\frac{966860414671188782939009282775}{35184372088832}\cdot t^{41}-\frac{445407606758637529219094163975}{8796093022208}\cdot t^{39}+\frac{1264548032981419192150761591975}{17592186044416}\cdot t^{37}-\frac{707721840307248052077653126265}{8796093022208}\cdot t^{35}+\frac{5073427650395332421520525423225}{70368744177664}\cdot t^{33}-\frac{229661333968512990274591685825}{4398046511104}\cdot t^{31}+\frac{270360810874325418930848440275}{8796093022208}\cdot t^{29}-\frac{64797219135168902057806650975}{4398046511104}\cdot t^{27}+\frac{101083661850863487210178375521}{17592186044416}\cdot t^{25}-\frac{7988698249541371486578902175}{4398046511104}\cdot t^{23}+\frac{4066681402684038201417429075}{8796093022208}\cdot t^{21}-\frac{412561881431714020433652225}{4398046511104}\cdot t^{19}+\frac{1052956443654076082002306425}{70368744177664}\cdot t^{17}-\frac{16199329902370401261573945}{8796093022208}\cdot t^{15}+\frac{2999875907846370603995175}{17592186044416}\cdot t^{13}-\frac{100944918383096163551175}{8796093022208}\cdot t^{11}+\frac{18820239020577250831575}{35184372088832}\cdot t^9-\frac{141505556545693615275}{8796093022208}\cdot t^7+\frac{4911763119767877555}{17592186044416}\cdot t^5-\frac{20146690401016725}{8796093022208}\cdot t^3+\frac{395033145117975}{70368744177664}\cdot t$

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.