DLMF:30.11.E11 (Q8906): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: DLMF:30.11.E4 / rank
 
Normal rank
Property / Symbols used: DLMF:30.11.E4 / qualifier
 
Defining formula:

A n m ⁢ ( γ 2 ) superscript subscript 𝐴 𝑛 𝑚 superscript 𝛾 2 {\displaystyle{\displaystyle A_{n}^{m}(\gamma^{2})}}

A_{n}^{m}(\gamma^{2})
Property / Symbols used: DLMF:30.11.E4 / qualifier
 
xml-id: C30.S11.XMD5.m1ddec

Revision as of 01:50, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:30.11.E11
No description defined

    Statements

    Defining formula
    K n m ⁢ ( γ ) = π 2 ⁢ ( γ 2 ) m + 1 ⁢ ( - 1 ) m ⁢ a n , 1 2 ⁢ ( m - n + 1 ) - m ⁢ ( γ 2 ) Γ ⁡ ( 5 2 + m ) ⁢ A n - m ⁢ ( γ 2 ) ⁢ ( d 𝖯𝗌 n m ⁡ ( z , γ 2 ) / d z | z = 0 ) , superscript subscript 𝐾 𝑛 𝑚 𝛾 𝜋 2 superscript 𝛾 2 𝑚 1 superscript 1 𝑚 superscript subscript 𝑎 𝑛 1 2 𝑚 𝑛 1 𝑚 superscript 𝛾 2 Euler-Gamma 5 2 𝑚 superscript subscript 𝐴 𝑛 𝑚 superscript 𝛾 2 evaluated-at derivative spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑧 superscript 𝛾 2 𝑧 𝑧 0 {\displaystyle{\displaystyle K_{n}^{m}(\gamma)=\frac{\sqrt{\pi}}{2}\left(\frac% {\gamma}{2}\right)^{m+1}\*\frac{(-1)^{m}a_{n,\frac{1}{2}(m-n+1)}^{-m}(\gamma^{% 2})}{\Gamma\left(\frac{5}{2}+m\right)A_{n}^{-m}(\gamma^{2})(\left.\ifrac{% \mathrm{d}\mathsf{Ps}^{m}_{n}(z,\gamma^{2})}{\mathrm{d}z}\right|_{z=0})},}}
    0 references
    DLMF id
    DLMF:30.11.E11
    0 references
    constraint
    n - m 𝑛 𝑚 {\displaystyle{\displaystyle n-m}}
    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.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    Q12418
    Defining formula
    𝖯𝗌 n m ⁡ ( x , γ 2 ) spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 {\displaystyle{\displaystyle\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},% \NVar{\gamma^{2}}\right)}}
    xml-id
    C30.S4.SS1.m1aadec
    0 references
    Q12401
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C30.S1.XMD1.m1gdec
    0 references
    Q12408
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C30.S1.XMD4.m1hdec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1ldec
    0 references
    DLMF:30.11.E4
    Defining formula
    A n m ⁢ ( γ 2 ) superscript subscript 𝐴 𝑛 𝑚 superscript 𝛾 2 {\displaystyle{\displaystyle A_{n}^{m}(\gamma^{2})}}
    xml-id
    C30.S11.XMD5.m1ddec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8906&oldid=35020"