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Fungrim entry: da16db

RF ⁣(0,y,z)=0π/21ycos2 ⁣(θ)+zsin2 ⁣(θ)dθR_F\!\left(0, y, z\right) = \int_{0}^{\pi / 2} \frac{1}{\sqrt{y \cos^{2}\!\left(\theta\right) + z \sin^{2}\!\left(\theta\right)}} \, 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_F\!\left(0, y, z\right) = \int_{0}^{\pi / 2} \frac{1}{\sqrt{y \cos^{2}\!\left(\theta\right) + z \sin^{2}\!\left(\theta\right)}} \, 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
CarlsonRFRF ⁣(x,y,z)R_F\!\left(x, y, z\right) Carlson symmetric elliptic integral of the first kind
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
Coscos(z)\cos(z) Cosine
Sinsin(z)\sin(z) Sine
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(CarlsonRF(0, y, z), Integral(Div(1, Sqrt(Add(Mul(y, Pow(Cos(theta), 2)), Mul(z, Pow(Sin(theta), 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