DLMF:11.6.E7 (Q3983): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1afdec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11497 / rank
 
Normal rank
Property / Symbols used: Q11497 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11497 / qualifier
 
xml-id: C11.S1.XMD5.m1edec
Property / Symbols used
 
Property / Symbols used: Q11498 / rank
 
Normal rank
Property / Symbols used: Q11498 / qualifier
 
Defining formula:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11498 / qualifier
 
xml-id: C11.S1.XMD6.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11499 / rank
 
Normal rank
Property / Symbols used: Q11499 / qualifier
 
Defining formula:

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

\lambda
Property / Symbols used: Q11499 / qualifier
 
xml-id: C11.S6.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11500 / rank
 
Normal rank
Property / Symbols used: Q11500 / qualifier
 
Defining formula:

c k ⁢ ( λ ) subscript 𝑐 𝑘 𝜆 {\displaystyle{\displaystyle c_{k}(\lambda)}}

c_{k}(\lambda)
Property / Symbols used: Q11500 / qualifier
 
xml-id: C11.S6.XMD2.m1adec

Latest revision as of 14:48, 2 January 2020

No description defined
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English
DLMF:11.6.E7
No description defined

    Statements

    Defining formula
    𝐌 ν ⁡ ( λ ⁢ ν ) ∼ - ( 1 2 ⁢ λ ⁢ ν ) ν - 1 π ⁢ Γ ⁡ ( ν + 1 2 ) ⁢ ∑ k = 0 ∞ k ! ⁢ c k ⁢ ( i ⁢ λ ) ν k , asymptotic-expansion associated-Struve-M 𝜈 𝜆 𝜈 superscript 1 2 𝜆 𝜈 𝜈 1 𝜋 Euler-Gamma 𝜈 1 2 superscript subscript 𝑘 0 𝑘 subscript 𝑐 𝑘 𝑖 𝜆 superscript 𝜈 𝑘 {\displaystyle{\displaystyle\mathbf{M}_{\nu}\left(\lambda\nu\right)\sim-\frac{% (\frac{1}{2}\lambda\nu)^{\nu-1}}{\sqrt{\pi}\Gamma\left(\nu+\frac{1}{2}\right)}% \sum_{k=0}^{\infty}\frac{k!c_{k}(i\lambda)}{\nu^{k}},}}
    0 references
    DLMF id
    DLMF:11.6.E7
    0 references
    constraint
    | ph ⁡ ν | ≤ 1 2 ⁢ π - δ phase 𝜈 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\nu|\leq\frac{1}{2}\pi-\delta}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    modified Struve function
    Defining formula
    𝐌 ν ⁡ ( z ) associated-Struve-M 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{M}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E6.m2abdec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aedec
    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
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1afdec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1ddec
    0 references
    Q11497
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1edec
    0 references
    Q11498
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C11.S1.XMD6.m1fdec
    0 references
    Q11499
    Defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C11.S6.XMD1.m1adec
    0 references
    Q11500
    Defining formula
    c k ⁢ ( λ ) subscript 𝑐 𝑘 𝜆 {\displaystyle{\displaystyle c_{k}(\lambda)}}
    xml-id
    C11.S6.XMD2.m1adec
    0 references
     
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