DLMF:14.11.E1 (Q4817): 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: cotangent function / rank
 
Normal rank
Property / Symbols used: cotangent function / qualifier
 
Defining formula:

cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}

\cot@@{\NVar{z}}
Property / Symbols used: cotangent function / qualifier
 
xml-id: C4.S14.E7.m2adec

Revision as of 01:39, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.11.E1
No description defined

    Statements

    Defining formula
    ∂ ∂ ⁡ ν ⁡ 𝖯 ν μ ⁡ ( x ) = π ⁢ cot ⁡ ( ν ⁢ π ) ⁢ 𝖯 ν μ ⁡ ( x ) - 1 π ⁢ 𝖠 ν μ ⁢ ( x ) , partial-derivative 𝜈 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝜋 𝜈 𝜋 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 1 𝜋 superscript subscript 𝖠 𝜈 𝜇 𝑥 {\displaystyle{\displaystyle\frac{\partial}{\partial\nu}\mathsf{P}^{\mu}_{\nu}% \left(x\right)=\pi\cot\left(\nu\pi\right)\mathsf{P}^{\mu}_{\nu}\left(x\right)-% \frac{1}{\pi}\mathsf{A}_{\nu}^{\mu}(x),}}
    0 references
    DLMF id
    DLMF:14.11.E1
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    cotangent function
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4817&oldid=33472"