DLMF:8.12.E7 (Q2602): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1edec
Property / Symbols used
 
Property / Symbols used: Q11330 / rank
 
Normal rank
Property / Symbols used: Q11330 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11330 / qualifier
 
xml-id: C8.S1.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q11348 / rank
 
Normal rank
Property / Symbols used: Q11348 / qualifier
 
Defining formula:

η ⁢ ( λ ) 𝜂 𝜆 {\displaystyle{\displaystyle\eta(\lambda)}}

\eta(\lambda)
Property / Symbols used: Q11348 / qualifier
 
xml-id: C8.S12.XMD1.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11349 / rank
 
Normal rank
Property / Symbols used: Q11349 / qualifier
 
Defining formula:

S ⁢ ( a , η ) 𝑆 𝑎 𝜂 {\displaystyle{\displaystyle S(a,\eta)}}

S(a,\eta)
Property / Symbols used: Q11349 / qualifier
 
xml-id: C8.S12.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11351 / rank
 
Normal rank
Property / Symbols used: Q11351 / qualifier
 
Defining formula:

c k ⁢ ( η ) subscript 𝑐 𝑘 𝜂 {\displaystyle{\displaystyle c_{k}(\eta)}}

c_{k}(\eta)
Property / Symbols used: Q11351 / qualifier
 
xml-id: C8.S12.XMD6.m1dec

Latest revision as of 13:57, 2 January 2020

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English
DLMF:8.12.E7
No description defined

    Statements

    Defining formula
    S ⁢ ( a , η ) ∼ e - 1 2 ⁢ a ⁢ η 2 2 ⁢ π ⁢ a ⁢ ∑ k = 0 ∞ c k ⁢ ( η ) ⁢ a - k , asymptotic-expansion 𝑆 𝑎 𝜂 superscript 𝑒 1 2 𝑎 superscript 𝜂 2 2 𝜋 𝑎 superscript subscript 𝑘 0 subscript 𝑐 𝑘 𝜂 superscript 𝑎 𝑘 {\displaystyle{\displaystyle S(a,\eta)\sim\frac{e^{-\frac{1}{2}a\eta^{2}}}{% \sqrt{2\pi a}}\sum_{k=0}^{\infty}c_{k}(\eta)a^{-k},}}
    0 references
    DLMF id
    DLMF:8.12.E7
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1edec
    0 references
    Q11330
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1dec
    0 references
    Q11348
    Defining formula
    η ⁢ ( λ ) 𝜂 𝜆 {\displaystyle{\displaystyle\eta(\lambda)}}
    xml-id
    C8.S12.XMD1.m1fdec
    0 references
    Q11349
    Defining formula
    S ⁢ ( a , η ) 𝑆 𝑎 𝜂 {\displaystyle{\displaystyle S(a,\eta)}}
    xml-id
    C8.S12.XMD3.m1bdec
    0 references
    Q11351
    Defining formula
    c k ⁢ ( η ) subscript 𝑐 𝑘 𝜂 {\displaystyle{\displaystyle c_{k}(\eta)}}
    xml-id
    C8.S12.XMD6.m1dec
    0 references
     
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