DLMF:14.20.E13 (Q4934): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11630 / rank
 
Normal rank
Property / Symbols used: Q11630 / qualifier
 
Defining formula:

τ 𝜏 {\displaystyle{\displaystyle\tau}}

\tau
Property / Symbols used: Q11630 / qualifier
 
xml-id: C14.S1.XMD3.m1tdec

Latest revision as of 13:35, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.20.E13
No description defined

    Statements

    Defining formula
    P - 1 2 + i ⁢ τ ⁡ ( x ) = cosh ⁡ ( τ ⁢ π ) π ⁢ ∫ 1 ∞ P - 1 2 + i ⁢ τ ⁡ ( t ) x + t ⁢ d t , shorthand-Legendre-P-first-kind 1 2 𝑖 𝜏 𝑥 𝜏 𝜋 𝜋 superscript subscript 1 shorthand-Legendre-P-first-kind 1 2 𝑖 𝜏 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle P_{-\frac{1}{2}+i\tau}\left(x\right)=\frac{\cosh% \left(\tau\pi\right)}{\pi}\int_{1}^{\infty}\frac{P_{-\frac{1}{2}+i\tau}\left(t% \right)}{x+t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:14.20.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.m2ahdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2asdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q11447
    Defining formula
    P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m3adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1rdec
    0 references
    Q11630
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C14.S1.XMD3.m1tdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4934&oldid=37919"