DLMF:11.6.E4 (Q3980)

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DLMF:11.6.E4
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    ∫ 0 z 𝐌 0 ⁡ ( t ) ⁢ d t + 2 π ⁢ ( ln ⁡ ( 2 ⁢ z ) + γ ) ∼ 2 π ⁢ ∑ k = 1 ∞ ( 2 ⁢ k ) ! ⁢ ( 2 ⁢ k - 1 ) ! ( k ! ) 2 ⁢ ( 2 ⁢ z ) 2 ⁢ k , asymptotic-expansion superscript subscript 0 𝑧 associated-Struve-M 0 𝑡 𝑡 2 𝜋 2 𝑧 2 𝜋 superscript subscript 𝑘 1 2 𝑘 2 𝑘 1 superscript 𝑘 2 superscript 2 𝑧 2 𝑘 {\displaystyle{\displaystyle\int_{0}^{z}\mathbf{M}_{0}\left(t\right)\mathrm{d}% t+\frac{2}{\pi}(\ln\left(2z\right)+\gamma)\sim\frac{2}{\pi}\sum_{k=1}^{\infty}% \frac{(2k)!(2k-1)!}{(k!)^{2}(2z)^{2k}},}}
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    DLMF:11.6.E4
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