DLMF:8.12.E15 (Q2617)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:8.12.E15
No description defined

    Statements

    Defining formula
    Q ⁡ ( a , a ) ∼ 1 2 + 1 2 ⁢ π ⁢ a ⁢ ∑ k = 0 ∞ c k ⁢ ( 0 ) ⁢ a - k , asymptotic-expansion incomplete-gamma-Q 𝑎 𝑎 1 2 1 2 𝜋 𝑎 superscript subscript 𝑘 0 subscript 𝑐 𝑘 0 superscript 𝑎 𝑘 {\displaystyle{\displaystyle Q\left(a,a\right)\sim\frac{1}{2}+\frac{1}{\sqrt{2% \pi a}}\sum_{k=0}^{\infty}c_{k}(0)a^{-k},}}
    0 references
    DLMF id
    DLMF:8.12.E15
    0 references
    constraint
    | ph ⁡ a | ≤ π - δ phase 𝑎 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\pi-\delta}}
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    Q11326
    Defining formula
    Q ⁡ ( a , z ) incomplete-gamma-Q 𝑎 𝑧 {\displaystyle{\displaystyle Q\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E4.m2abdec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1gdec
    0 references
    Q11330
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1edec
    0 references
    Q11343
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C8.S1.XMD7.m1dec
    0 references
    Q11351
    Defining formula
    c k ⁢ ( η ) subscript 𝑐 𝑘 𝜂 {\displaystyle{\displaystyle c_{k}(\eta)}}
    xml-id
    C8.S12.XMD6.m1edec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2617&oldid=42161"