DLMF:8.11.E5 (Q2576): Difference between revisions

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Property / constraint
 

| ph ⁡ a | ≤ π - δ ph 𝑎 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\pi-\delta}}

|\operatorname{ph}a|\leq\pi-\delta
Property / constraint: | ph ⁡ a | ≤ π - δ ph 𝑎 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\pi-\delta}} / rank
 
Normal rank

Revision as of 16:10, 30 December 2019

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DLMF:8.11.E5
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    Statements

    test
    P ⁡ ( a , z ) ∼ z a ⁢ e - z Γ ⁡ ( 1 + a ) ∼ ( 2 ⁢ π ⁢ a ) - 1 2 ⁢ e a - z ⁢ ( z / a ) a , asymptotically-equals incomplete-gamma-P 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 Euler-Gamma 1 𝑎 asymptotically-equals superscript 2 𝜋 𝑎 1 2 superscript 𝑒 𝑎 𝑧 superscript 𝑧 𝑎 𝑎 {\displaystyle{\displaystyle P\left(a,z\right)\sim\frac{z^{a}e^{-z}}{\Gamma% \left(1+a\right)}\sim(2\pi a)^{-\frac{1}{2}}e^{a-z}(z/a)^{a},}}
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    DLMF id
    DLMF:8.11.E5
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    constraint
    | ph ⁡ a | ≤ π - δ phase 𝑎 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\pi-\delta}}
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    a → ∞ → 𝑎 {\displaystyle{\displaystyle a\to\infty}}
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    | ph ⁡ a | ≤ π - δ ph 𝑎 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\pi-\delta}}
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