DLMF:11.10.E22 (Q4041): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1udec
Property / Symbols used
 
Property / Symbols used: Q11493 / rank
 
Normal rank
Property / Symbols used: Q11493 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11493 / qualifier
 
xml-id: C11.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q11497 / rank
 
Normal rank
Property / Symbols used: Q11497 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11497 / qualifier
 
xml-id: C11.S1.XMD5.m1bdec

Latest revision as of 14:57, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:11.10.E22
No description defined

    Statements

    Defining formula
    𝐄 n ⁡ ( z ) = - 𝐇 n ⁡ ( z ) + 1 π ⁢ ∑ k = 0 m 1 Γ ⁡ ( k + 1 2 ) Γ ⁡ ( n + 1 2 - k ) ⁢ ( 1 2 ⁢ z ) n - 2 ⁢ k - 1 , Weber-E 𝑛 𝑧 Struve-H 𝑛 𝑧 1 𝜋 superscript subscript 𝑘 0 subscript 𝑚 1 Euler-Gamma 𝑘 1 2 Euler-Gamma 𝑛 1 2 𝑘 superscript 1 2 𝑧 𝑛 2 𝑘 1 {\displaystyle{\displaystyle\mathbf{E}_{n}\left(z\right)=-\mathbf{H}_{n}\left(% z\right)+\frac{1}{\pi}\sum_{k=0}^{m_{1}}\frac{\Gamma\left(k+\tfrac{1}{2}\right% )}{\Gamma\left(n\!+\!\tfrac{1}{2}\!-\!k\right)}(\tfrac{1}{2}z)^{n-2k-1},}}
    0 references
    DLMF id
    DLMF:11.10.E22
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    Struve function
    Defining formula
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2adec
    0 references
    Weber function
    Defining formula
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2amdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aqdec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1udec
    0 references
    Q11493
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C11.S1.XMD4.m1dec
    0 references
    Q11497
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4041&oldid=52698"