DLMF:13.6.E11 (Q4398): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(One intermediate revision by the same user not shown)
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
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1jdec

Latest revision as of 15:51, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.6.E11
No description defined

    Statements

    Defining formula
    U ⁡ ( 5 6 , 5 3 , 4 3 ⁢ z 3 / 2 ) = π ⁢ 3 5 / 6 ⁢ exp ⁡ ( 2 3 ⁢ z 3 / 2 ) 2 2 / 3 ⁢ z ⁢ Ai ⁡ ( z ) . Kummer-confluent-hypergeometric-U 5 6 5 3 4 3 superscript 𝑧 3 2 𝜋 superscript 3 5 6 2 3 superscript 𝑧 3 2 superscript 2 2 3 𝑧 Airy-Ai 𝑧 {\displaystyle{\displaystyle U\left(\tfrac{5}{6},\tfrac{5}{3},\tfrac{4}{3}z^{3% /2}\right)=\sqrt{\pi}\frac{3^{5/6}\exp\left(\tfrac{2}{3}z^{3/2}\right)}{2^{2/3% }z}\mathrm{Ai}\left(z\right).}}
    0 references
    DLMF id
    DLMF:13.6.E11
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1adec
    0 references
    Kummer confluent hypergeometric function
    Defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1jdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4398&oldid=61535"