DLMF:10.22.E36 (Q3410)

From DRMF
Revision as of 14:52, 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.E36
No description defined

    Statements

    Defining formula
    1 Γ ⁡ ( α ) ⁢ ∫ 0 x ( x - t ) α - 1 ⁢ J ν ⁡ ( t ) ⁢ d t = 2 α ⁢ ∑ k = 0 ∞ ( α ) k k ! ⁢ J ν + α + 2 ⁢ k ⁡ ( x ) , 1 Euler-Gamma 𝛼 superscript subscript 0 𝑥 superscript 𝑥 𝑡 𝛼 1 Bessel-J 𝜈 𝑡 𝑡 superscript 2 𝛼 superscript subscript 𝑘 0 subscript 𝛼 𝑘 𝑘 Bessel-J 𝜈 𝛼 2 𝑘 𝑥 {\displaystyle{\displaystyle\frac{1}{\Gamma\left(\alpha\right)}\int_{0}^{x}(x-% t)^{\alpha-1}J_{\nu}\left(t\right)\mathrm{d}t=2^{\alpha}\sum_{k=0}^{\infty}% \frac{(\alpha)_{k}}{k!}J_{\nu+\alpha+2k}\left(x\right),}}
    0 references
    DLMF id
    DLMF:10.22.E36
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3410&oldid=9409"