DLMF:1.14.E47 (Q539): Difference between revisions

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𝒮 ⁡ ( f ) ⁡ ( s ) = 𝒮 ⁡ f ⁡ ( s ) = ∫ 0 ∞ f ⁢ ( t ) s + t ⁢ d t . Stieltjes-transform 𝑓 𝑠 Stieltjes-transform 𝑓 𝑠 subscript superscript 0 𝑓 𝑡 𝑠 𝑡 𝑡 {\displaystyle{\displaystyle\mathcal{S}\left(f\right)\left(s\right)=\mathcal{S% }\mskip-3.0mu f\mskip 3.0mu \left(s\right)=\int^{\infty}_{0}\frac{f(t)}{s+t}% \mathrm{d}t.}}

\Stieltjestrans@{f}@{s}=\Stieltjestrans@@{f}@{s}=\int^{\infty}_{0}\frac{f(t)}{s+t}\diff{t}.

𝒮 ⁡ ( f ) ⁡ ( s ) = 𝒮 ⁡ f ⁡ ( s ) = ∫ 0 ∞ f ⁢ ( t ) s + t ⁢ d t Stieltjes-transform 𝑓 𝑠 Stieltjes-transform 𝑓 𝑠 subscript superscript 0 𝑓 𝑡 𝑠 𝑡 𝑡 {\displaystyle{\displaystyle\mathcal{S}\left(f\right)\left(s\right)=\mathcal{S% }\mskip-3.0mu f\mskip 3.0mu \left(s\right)=\int^{\infty}_{0}\frac{f(t)}{s+t}% \mathrm{d}t}}

\Stieltjestrans@{f}@{s}=\Stieltjestrans@@{f}@{s}=\int^{\infty}_{0}\frac{f(t)}{s+t}\diff{t}

Revision as of 14:54, 30 December 2019

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DLMF:1.14.E47
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    test
    𝒮 ⁡ ( f ) ⁡ ( s ) = 𝒮 ⁡ f ⁡ ( s ) = ∫ 0 ∞ f ⁢ ( t ) s + t ⁢ d t Stieltjes-transform 𝑓 𝑠 Stieltjes-transform 𝑓 𝑠 subscript superscript 0 𝑓 𝑡 𝑠 𝑡 𝑡 {\displaystyle{\displaystyle\mathcal{S}\left(f\right)\left(s\right)=\mathcal{S% }\mskip-3.0mu f\mskip 3.0mu \left(s\right)=\int^{\infty}_{0}\frac{f(t)}{s+t}% \mathrm{d}t}}
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    DLMF id
    DLMF:1.14.E47
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