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Formula:7040

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Digital Library of Mathematical Functions ID 19.18.E2

d d x ⁑ R G ⁑ ( x + a , x + b , x + c ) = 1 2 ⁒ R F ⁑ ( x + a , x + b , x + c ) . derivative π‘₯ Carlson-integral-RG π‘₯ π‘Ž π‘₯ 𝑏 π‘₯ 𝑐 1 2 Carlson-integral-RF π‘₯ π‘Ž π‘₯ 𝑏 π‘₯ 𝑐 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}R_{G}\left(x+a,x+b,x% +c\right)=\tfrac{1}{2}R_{F}\left(x+a,x+b,x+c\right).}}


Constraint(s)

Symbols List

  • R F ⁑ ( x , y , z ) Carlson-integral-RF π‘₯ 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}} : symmetric elliptic integral of first kind
  • R G ⁑ ( x , y , z ) Carlson-integral-RG π‘₯ 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}} : symmetric elliptic integral of second kind
  • d f d x derivative 𝑓 π‘₯ {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}} : derivative of $$f$$ with respect to $$x$$
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