DLMF:14.5.E23 (Q4735): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11596 / rank
 
Normal rank
Property / Symbols used: Q11596 / qualifier
 
Defining formula:

𝖰 ν ⁡ ( x ) = 𝖰 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 Ferrers-Legendre-Q-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{Q}^{0}_{\nu}\left(x\right)}}

\FerrersQ[]{\NVar{\nu}}@{\NVar{x}}=\FerrersQ[0]{\nu}@{x}
Property / Symbols used: Q11596 / qualifier
 
xml-id: C14.S2.SS2.p2.m4acdec
Property / Symbols used
 
Property / Symbols used: Q11598 / rank
 
Normal rank
Property / Symbols used: Q11598 / qualifier
 
Defining formula:

0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}}

0<\theta<\pi
Property / Symbols used: Q11598 / qualifier
 
xml-id: C14.S5.XMD2.m1hdec

Latest revision as of 01:24, 2 January 2020

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DLMF:14.5.E23
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    Statements

    Defining formula
    𝖰 - 1 2 ⁡ ( cos ⁡ θ ) = K ⁡ ( cos ⁡ ( 1 2 ⁢ θ ) ) . shorthand-Ferrers-Legendre-Q-first-kind 1 2 𝜃 complete-elliptic-integral-first-kind-K 1 2 𝜃 {\displaystyle{\displaystyle\mathsf{Q}_{-\frac{1}{2}}\left(\cos\theta\right)=K% \left(\cos\left(\tfrac{1}{2}\theta\right)\right).}}
    0 references
    DLMF id
    DLMF:14.5.E23
    0 references
    Symbols used
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1acdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aidec
    0 references
    Q11596
    Defining formula
    𝖰 ν ⁡ ( x ) = 𝖰 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 Ferrers-Legendre-Q-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{Q}^{0}_{\nu}\left(x\right)}}
    xml-id
    C14.S2.SS2.p2.m4acdec
    0 references
    Q11598
    Defining formula
    0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}}
    xml-id
    C14.S5.XMD2.m1hdec
    0 references
     
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