DLMF:2.3.E32 (Q752): Difference between revisions

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Property / constraint
 

x → ∞ → 𝑥 {\displaystyle{\displaystyle x\to\infty}}

x\to\infty
Property / constraint: x → ∞ → 𝑥 {\displaystyle{\displaystyle x\to\infty}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11aldec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2andec
Property / Symbols used
 
Property / Symbols used: integral (locally) / rank
 
Normal rank
Property / Symbols used: integral (locally) / qualifier
 
test:

I ⁢ ( α , x ) 𝐼 𝛼 𝑥 {\displaystyle{\displaystyle I(\alpha,x)}}

I(\alpha,x)
Property / Symbols used: integral (locally) / qualifier
 
xml-id: C2.S3.XMD27.m1bdec
Property / Symbols used
 
Property / Symbols used: Q10964 / rank
 
Normal rank
Property / Symbols used: Q10964 / qualifier
 
test:

p ⁢ ( α , t ) 𝑝 𝛼 𝑡 {\displaystyle{\displaystyle p(\alpha,t)}}

p(\alpha,t)
Property / Symbols used: Q10964 / qualifier
 
xml-id: C2.S3.XMD28.m1fdec
Property / Symbols used
 
Property / Symbols used: Q10967 / rank
 
Normal rank
Property / Symbols used: Q10967 / qualifier
 
test:

a ⁢ ( α ) 𝑎 𝛼 {\displaystyle{\displaystyle a(\alpha)}}

a(\alpha)
Property / Symbols used: Q10967 / qualifier
 
xml-id: C2.S3.XMD31.m1ddec
Property / Symbols used
 
Property / Symbols used: Q10970 / rank
 
Normal rank
Property / Symbols used: Q10970 / qualifier
 
test:

ϕ s ⁢ ( α ) subscript italic-ϕ 𝑠 𝛼 {\displaystyle{\displaystyle\phi_{s}(\alpha)}}

\phi_{s}(\alpha)
Property / Symbols used: Q10970 / qualifier
 
xml-id: C2.S3.XMD35.m1adec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
test:

F s ⁢ ( y ) subscript 𝐹 𝑠 𝑦 {\displaystyle{\displaystyle F_{s}(y)}}

F_{s}(y)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C2.S3.XMD36.m1dec
Property / Symbols used
 
Property / Symbols used: Q10950 / rank
 
Normal rank
Property / Symbols used: Q10950 / qualifier
 
test:

λ 𝜆 {\displaystyle{\displaystyle\lambda}}

\lambda
Property / Symbols used: Q10950 / qualifier
 
xml-id: C2.S3.XMD8.m1ndec

Latest revision as of 15:56, 1 January 2020

No description defined
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English
DLMF:2.3.E32
No description defined

    Statements

    test
    I ⁢ ( α , x ) ∼ e - x ⁢ p ⁢ ( α , 0 ) x λ / 2 ⁢ ∑ s = 0 ∞ ϕ s ⁢ ( α ) ⁢ F s ⁢ ( a ⁢ x ) x s / 2 , asymptotic-expansion 𝐼 𝛼 𝑥 superscript 𝑒 𝑥 𝑝 𝛼 0 superscript 𝑥 𝜆 2 superscript subscript 𝑠 0 subscript italic-ϕ 𝑠 𝛼 subscript 𝐹 𝑠 𝑎 𝑥 superscript 𝑥 𝑠 2 {\displaystyle{\displaystyle I(\alpha,x)\sim\frac{e^{-xp(\alpha,0)}}{x^{% \lambda/2}}\sum_{s=0}^{\infty}\phi_{s}(\alpha)\frac{F_{s}(a\sqrt{x})}{x^{s/2}}% ,}}
    0 references
    DLMF id
    DLMF:2.3.E32
    0 references
    constraint
    x → ∞ → 𝑥 {\displaystyle{\displaystyle x\to\infty}}
    0 references
    Symbols used
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aldec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2andec
    0 references
    integral (locally)
    test
    I ⁢ ( α , x ) 𝐼 𝛼 𝑥 {\displaystyle{\displaystyle I(\alpha,x)}}
    xml-id
    C2.S3.XMD27.m1bdec
    0 references
    Q10964
    test
    p ⁢ ( α , t ) 𝑝 𝛼 𝑡 {\displaystyle{\displaystyle p(\alpha,t)}}
    xml-id
    C2.S3.XMD28.m1fdec
    0 references
    Q10967
    test
    a ⁢ ( α ) 𝑎 𝛼 {\displaystyle{\displaystyle a(\alpha)}}
    xml-id
    C2.S3.XMD31.m1ddec
    0 references
    Q10970
    test
    ϕ s ⁢ ( α ) subscript italic-ϕ 𝑠 𝛼 {\displaystyle{\displaystyle\phi_{s}(\alpha)}}
    xml-id
    C2.S3.XMD35.m1adec
    0 references
    function (locally)
    test
    F s ⁢ ( y ) subscript 𝐹 𝑠 𝑦 {\displaystyle{\displaystyle F_{s}(y)}}
    xml-id
    C2.S3.XMD36.m1dec
    0 references
    Q10950
    test
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C2.S3.XMD8.m1ndec
    0 references
     
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