DLMF:10.65#Ex6 (Q3838)

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DLMF:10.65#Ex6
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    Defining formula
    kei ⁡ x = - ln ⁡ ( 1 2 ⁢ x ) ⁢ bei ⁡ x - 1 4 ⁢ π ⁢ ber ⁡ x + ∑ k = 0 ∞ ( - 1 ) k ⁢ ψ ⁡ ( 2 ⁢ k + 2 ) ( ( 2 ⁢ k + 1 ) ! ) 2 ⁢ ( 1 4 ⁢ x 2 ) 2 ⁢ k + 1 . Kelvin-kei 𝑥 1 2 𝑥 Kelvin-bei 𝑥 1 4 𝜋 Kelvin-ber 𝑥 superscript subscript 𝑘 0 superscript 1 𝑘 digamma 2 𝑘 2 superscript 2 𝑘 1 2 superscript 1 4 superscript 𝑥 2 2 𝑘 1 {\displaystyle{\displaystyle\operatorname{kei}x=-\ln\left(\tfrac{1}{2}x\right)% \operatorname{bei}x-\tfrac{1}{4}\pi\operatorname{ber}x+\sum_{k=0}^{\infty}(-1)% ^{k}\frac{\psi\left(2k+2\right)}{((2k+1)!)^{2}}(\tfrac{1}{4}x^{2})^{2k+1}.}}
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    DLMF id
    DLMF:10.65#Ex6
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