DLMF:10.18.E13 (Q3206): Difference between revisions

From DRMF
Jump to navigation Jump to search
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m2aedec
Property / Symbols used
 
Property / Symbols used: modulus of Bessel functions / rank
 
Normal rank
Property / Symbols used: modulus of Bessel functions / qualifier
 
Defining formula:

M ν ⁡ ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}

\HankelmodM{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: modulus of Bessel functions / qualifier
 
xml-id: C10.S18.E1.m2ahdec
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.m1ldec
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.m1ldec

Latest revision as of 15:34, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.18.E13
No description defined

    Statements

    Defining formula
    x 2 ⁢ M ν ′′ ⁡ ( x ) + x ⁢ M ν ′ ⁡ ( x ) + ( x 2 - ν 2 ) ⁢ M ν ⁡ ( x ) = 4 π 2 ⁢ M ν 3 ⁢ ( x ) , superscript 𝑥 2 diffop modulus-Bessel-M 𝜈 2 𝑥 𝑥 diffop modulus-Bessel-M 𝜈 1 𝑥 superscript 𝑥 2 superscript 𝜈 2 modulus-Bessel-M 𝜈 𝑥 4 superscript 𝜋 2 modulus-Bessel-M 𝜈 3 𝑥 {\displaystyle{\displaystyle x^{2}M_{\nu}''\left(x\right)+xM_{\nu}'\left(x% \right)+(x^{2}-\nu^{2})M_{\nu}\left(x\right)=\frac{4}{\pi^{2}{{M_{\nu}^{3}}(x)% }},}}
    0 references
    DLMF id
    DLMF:10.18.E13
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    modulus of Bessel functions
    Defining formula
    M ν ⁡ ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E1.m2ahdec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1ldec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ldec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3206&oldid=58997"