DLMF:18.11.E8 (Q5642): 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
 
test:

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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11750 / rank
 
Normal rank
Property / Symbols used: Q11750 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11750 / qualifier
 
xml-id: C18.S1.XMD2.m1cdec

Latest revision as of 14:30, 2 January 2020

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English
DLMF:18.11.E8
No description defined

    Statements

    test
    lim n → ∞ ⁡ ( - 1 ) n 2 2 ⁢ n ⁢ n ! ⁢ H 2 ⁢ n + 1 ⁡ ( z 2 ⁢ n 1 2 ) = 2 π 1 2 ⁢ sin ⁡ z . subscript → 𝑛 superscript 1 𝑛 superscript 2 2 𝑛 𝑛 Hermite-polynomial-H 2 𝑛 1 𝑧 2 superscript 𝑛 1 2 2 superscript 𝜋 1 2 𝑧 {\displaystyle{\displaystyle\lim_{n\to\infty}\frac{(-1)^{n}}{2^{2n}n!}H_{2n+1}% \left(\frac{z}{2n^{\frac{1}{2}}}\right)=\frac{2}{\pi^{\frac{1}{2}}}\sin z.}}
    0 references
    DLMF id
    DLMF:18.11.E8
    0 references
    Symbols used
    Q10922
    test
    H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r13.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q11750
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1cdec
    0 references
     
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