DLMF:18.26.E8 (Q5938): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1gdec

Revision as of 01:44, 2 January 2020

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DLMF:18.26.E8
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    Statements

    Defining formula
    lim t → ∞ ⁡ S n ⁡ ( ( x - t ) 2 ; λ + i ⁢ t , λ - i ⁢ t , t ⁢ cot ⁡ ϕ ) / t n = n ! ⁢ ( csc ⁡ ϕ ) n ⁢ P n ( λ ) ⁡ ( x ; ϕ ) . subscript → 𝑡 continuous-dual-Hahn-S 𝑛 superscript 𝑥 𝑡 2 𝜆 𝑖 𝑡 𝜆 𝑖 𝑡 𝑡 italic-ϕ superscript 𝑡 𝑛 𝑛 superscript italic-ϕ 𝑛 Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle\lim_{t\to\infty}\ifrac{S_{n}\left((x-t)^{2};% \lambda+it,\lambda-it,t\cot\phi\right)}{t^{n}}=n!(\csc\phi)^{n}P^{(\lambda)}_{% n}\left(x;\phi\right).}}
    0 references
    DLMF id
    DLMF:18.26.E8
    0 references
    Symbols used
    Q11664
    Defining formula
    P n ( λ ) ⁡ ( x ; ϕ ) Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{\phi}\right)}}
    xml-id
    C18.S19.Px3.p1.m2adec
    0 references
    Q11784
    Defining formula
    S n ⁡ ( x ; a , b , c ) continuous-dual-Hahn-S 𝑛 𝑥 𝑎 𝑏 𝑐 {\displaystyle{\displaystyle S_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{c}\right)}}
    xml-id
    C18.S25.T1.t1.r3.m2abdec
    0 references
    cosecant function
    Defining formula
    csc ⁡ z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    xml-id
    C4.S14.E5.m2adec
    0 references
    cotangent function
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1gdec
    0 references
     
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