DLMF:10.38.E1 (Q3560)

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DLMF:10.38.E1
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    test
    ∂ ⁡ I ± ν ⁡ ( z ) ∂ ⁡ ν = ± I ± ν ⁡ ( z ) ⁢ ln ⁡ ( 1 2 ⁢ z ) ∓ ( 1 2 ⁢ z ) ± ν ⁢ ∑ k = 0 ∞ ψ ⁡ ( k + 1 ± ν ) Γ ⁡ ( k + 1 ± ν ) ⁢ ( 1 4 ⁢ z 2 ) k k ! , partial-derivative modified-Bessel-first-kind plus-or-minus 𝜈 𝑧 𝜈 minus-or-plus plus-or-minus modified-Bessel-first-kind plus-or-minus 𝜈 𝑧 1 2 𝑧 superscript 1 2 𝑧 plus-or-minus 𝜈 superscript subscript 𝑘 0 digamma plus-or-minus 𝑘 1 𝜈 Euler-Gamma plus-or-minus 𝑘 1 𝜈 superscript 1 4 superscript 𝑧 2 𝑘 𝑘 {\displaystyle{\displaystyle\frac{\partial I_{\pm\nu}\left(z\right)}{\partial% \nu}=\pm I_{\pm\nu}\left(z\right)\ln\left(\tfrac{1}{2}z\right)\mp(\tfrac{1}{2}% z)^{\pm\nu}\sum_{k=0}^{\infty}\frac{\psi\left(k+1\pm\nu\right)}{\Gamma\left(k+% 1\pm\nu\right)}\frac{(\frac{1}{4}z^{2})^{k}}{k!},}}
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    DLMF id
    DLMF:10.38.E1
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