DLMF:10.22.E71 (Q3445)

From DRMF
Revision as of 14:53, 29 December 2019 by Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.22.E71
No description defined

    Statements

    0 J μ ( a t ) J ν ( b t ) J ν ( c t ) t 1 - μ d t = ( b c ) μ - 1 ( sin ϕ ) μ - 1 2 ( 2 π ) 1 2 a μ 𝖯 ν - 1 2 1 2 - μ ( cos ϕ ) , superscript subscript 0 Bessel-J 𝜇 𝑎 𝑡 Bessel-J 𝜈 𝑏 𝑡 Bessel-J 𝜈 𝑐 𝑡 superscript 𝑡 1 𝜇 𝑡 superscript 𝑏 𝑐 𝜇 1 superscript italic-ϕ 𝜇 1 2 superscript 2 𝜋 1 2 superscript 𝑎 𝜇 Ferrers-Legendre-P-first-kind 1 2 𝜇 𝜈 1 2 italic-ϕ {\displaystyle{\displaystyle\int_{0}^{\infty}J_{\mu}\left(at\right)J_{\nu}% \left(bt\right)J_{\nu}\left(ct\right)t^{1-\mu}\mathrm{d}t=\frac{(bc)^{\mu-1}(% \sin\phi)^{\mu-\frac{1}{2}}}{(2\pi)^{\frac{1}{2}}a^{\mu}}\mathsf{P}^{\frac{1}{% 2}-\mu}_{\nu-\frac{1}{2}}(\cos\phi),}}
    0 references
    DLMF:10.22.E71
    0 references