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Fungrim entry: 9a0bc8

RD ⁣(0,y,z)=30π/2sin2 ⁣(θ)(ycos2 ⁣(θ)+zsin2 ⁣(θ))3/2dθR_D\!\left(0, y, z\right) = 3 \int_{0}^{\pi / 2} \frac{\sin^{2}\!\left(\theta\right)}{{\left(y \cos^{2}\!\left(\theta\right) + z \sin^{2}\!\left(\theta\right)\right)}^{3 / 2}} \, d\theta
Assumptions:yC  and  zC  and  Re(y)>0  and  Re(z)>0y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(y) > 0 \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0
R_D\!\left(0, y, z\right) = 3 \int_{0}^{\pi / 2} \frac{\sin^{2}\!\left(\theta\right)}{{\left(y \cos^{2}\!\left(\theta\right) + z \sin^{2}\!\left(\theta\right)\right)}^{3 / 2}} \, d\theta

y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(y) > 0 \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0
Fungrim symbol Notation Short description
CarlsonRDRD ⁣(x,y,z)R_D\!\left(x, y, z\right) Degenerate Carlson symmetric elliptic integral of the third kind
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Powab{a}^{b} Power
Sinsin(z)\sin(z) Sine
Coscos(z)\cos(z) Cosine
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
    Formula(Equal(CarlsonRD(0, y, z), Mul(3, Integral(Div(Pow(Sin(theta), 2), Pow(Add(Mul(y, Pow(Cos(theta), 2)), Mul(z, Pow(Sin(theta), 2))), Div(3, 2))), For(theta, 0, Div(Pi, 2)))))),
    Variables(y, z),
    Assumptions(And(Element(y, CC), Element(z, CC), Greater(Re(y), 0), Greater(Re(z), 0))))

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2021-03-15 19:12:00.328586 UTC