DLMF:10.65#Ex1 (Q3831)

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DLMF:10.65#Ex1
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    Defining formula
    ber ν ⁡ x = ( 1 2 ⁢ x ) ν ⁢ ∑ k = 0 ∞ cos ⁡ ( 3 4 ⁢ ν ⁢ π + 1 2 ⁢ k ⁢ π ) k ! ⁢ Γ ⁡ ( ν + k + 1 ) ⁢ ( 1 4 ⁢ x 2 ) k , Kelvin-ber 𝜈 𝑥 superscript 1 2 𝑥 𝜈 superscript subscript 𝑘 0 3 4 𝜈 𝜋 1 2 𝑘 𝜋 𝑘 Euler-Gamma 𝜈 𝑘 1 superscript 1 4 superscript 𝑥 2 𝑘 {\displaystyle{\displaystyle\operatorname{ber}_{\nu}x=(\tfrac{1}{2}x)^{\nu}% \sum_{k=0}^{\infty}\frac{\cos\left(\frac{3}{4}\nu\pi+\frac{1}{2}k\pi\right)}{k% !\Gamma\left(\nu+k+1\right)}(\tfrac{1}{4}x^{2})^{k},}}
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    DLMF id
    DLMF:10.65#Ex1
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