DLMF:2.10.E24 (Q1011): Difference between revisions

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Property / constraint
 

x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}

x\to+\infty
Property / constraint: x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11125 / rank
 
Normal rank
Property / Symbols used: Q11125 / qualifier
 
Defining formula:

F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}

\genhyperF{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{z}}
Property / Symbols used: Q11125 / qualifier
 
xml-id: C16.S2.m1abdec
Property / Symbols used
 
Property / Symbols used: asymptotic equality / rank
 
Normal rank
Property / Symbols used: asymptotic equality / qualifier
 
Defining formula:

∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}

\asympeq
Property / Symbols used: asymptotic equality / qualifier
 
xml-id: C2.S1.E1.m2adec
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.m2afdec
Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
Defining formula:

exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2adec

Latest revision as of 17:36, 1 January 2020

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DLMF:2.10.E24
No description defined

    Statements

    Defining formula
    F 2 0 ⁡ ( - ; 1 , 1 ; x ) ∼ exp ⁡ ( 3 ⁢ x 1 / 3 ) 2 ⁢ π ⁢ 3 1 / 2 ⁢ x 1 / 3 , asymptotically-equals Gauss-hypergeometric-pFq 0 2 1 1 𝑥 3 superscript 𝑥 1 3 2 𝜋 superscript 3 1 2 superscript 𝑥 1 3 {\displaystyle{\displaystyle{{}_{0}F_{2}}\left(-;1,1;x\right)\sim\frac{\exp% \left(3x^{1/3}\right)}{2\pi 3^{1/2}x^{1/3}},}}
    0 references
    DLMF id
    DLMF:2.10.E24
    0 references
    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
    0 references
    Symbols used
    Q11125
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1abdec
    0 references
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    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
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
     
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