DLMF:13.11.E1 (Q4476)

From DRMF
Revision as of 15:27, 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:13.11.E1
No description defined

    Statements

    Defining formula
    M ⁡ ( a , b , z ) = Γ ⁡ ( a - 1 2 ) ⁢ e 1 2 ⁢ z ⁢ ( 1 4 ⁢ z ) 1 2 - a ⁢ ∑ s = 0 ∞ ( 2 ⁢ a - 1 ) s ⁢ ( 2 ⁢ a - b ) s ( b ) s ⁢ s ! ⁢ ( a - 1 2 + s ) ⁢ I a - 1 2 + s ⁡ ( 1 2 ⁢ z ) , Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 Euler-Gamma 𝑎 1 2 superscript 𝑒 1 2 𝑧 superscript 1 4 𝑧 1 2 𝑎 superscript subscript 𝑠 0 Pochhammer 2 𝑎 1 𝑠 Pochhammer 2 𝑎 𝑏 𝑠 Pochhammer 𝑏 𝑠 𝑠 𝑎 1 2 𝑠 modified-Bessel-first-kind 𝑎 1 2 𝑠 1 2 𝑧 {\displaystyle{\displaystyle M\left(a,b,z\right)=\Gamma\left(a-\tfrac{1}{2}% \right)e^{\frac{1}{2}z}\left(\tfrac{1}{4}z\right)^{\frac{1}{2}-a}\*\sum_{s=0}^% {\infty}\frac{{\left(2a-1\right)_{s}}{\left(2a-b\right)_{s}}}{{\left(b\right)_% {s}}s!}\*\left(a-\tfrac{1}{2}+s\right)\*I_{a-\frac{1}{2}+s}\left(\tfrac{1}{2}z% \right),}}
    0 references
    DLMF id
    DLMF:13.11.E1
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4476&oldid=10475"