DLMF:10.23.E21 (Q3475): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
 
Defining formula:

J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the first kind / qualifier
 
xml-id: C10.S2.E2.m2aodec
Property / Symbols used
 
Property / Symbols used: Q11456 / rank
 
Normal rank
Property / Symbols used: Q11456 / qualifier
 
Defining formula:

j ν , m zero-Bessel-J 𝜈 𝑚 {\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}

\zBesselj{\NVar{\nu}}{\NVar{m}}
Property / Symbols used: Q11456 / qualifier
 
xml-id: C10.S21.SS1.p2.m11aadec
Property / Symbols used
 
Property / Symbols used: Q11438 / rank
 
Normal rank
Property / Symbols used: Q11438 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11438 / qualifier
 
xml-id: C10.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1idec

Latest revision as of 13:33, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.23.E21
No description defined

    Statements

    x ν = m = 1 2 J ν ( j ν , m x ) j ν , m J ν + 1 ( j ν , m ) , superscript 𝑥 𝜈 superscript subscript 𝑚 1 2 Bessel-J 𝜈 subscript 𝑗 𝜈 𝑚 𝑥 zero-Bessel-J 𝜈 𝑚 Bessel-J 𝜈 1 subscript 𝑗 𝜈 𝑚 {\displaystyle{\displaystyle x^{\nu}=\sum_{m=1}^{\infty}\frac{2J_{\nu}\left(j_% {\nu,m}x\right)}{j_{\nu,m}J_{\nu+1}\left(j_{\nu,m}\right)},}}
    0 references
    DLMF:10.23.E21
    0 references
    ν > 0 , 0 x < 1 formulae-sequence 𝜈 0 0 𝑥 1 {\displaystyle{\displaystyle\nu>0,0\leq x<1}}
    0 references
    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2aodec
    0 references
    j ν , m zero-Bessel-J 𝜈 𝑚 {\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}
    C10.S21.SS1.p2.m11aadec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C10.S1.XMD1.m1bdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C10.S1.XMD4.m1bdec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1idec
    0 references