DLMF:19.30.E12 (Q6687): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11242 / rank
 
Normal rank
Property / Symbols used: Q11242 / qualifier
 
Defining formula:

arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}

\asin@@{\NVar{z}}
Property / Symbols used: Q11242 / qualifier
 
xml-id: C4.S23.SS2.p1.m5adec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
Defining formula:

tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2adec
Property / Symbols used
 
Property / Symbols used: Q11807 / rank
 
Normal rank
Property / Symbols used: Q11807 / qualifier
 
Defining formula:

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

\phi
Property / Symbols used: Q11807 / qualifier
 
xml-id: C19.S1.XMD4.m1edec
Property / Symbols used
 
Property / Symbols used: Q11919 / rank
 
Normal rank
Property / Symbols used: Q11919 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11919 / qualifier
 
xml-id: C19.S30.XMD5.m1adec
Property / Symbols used
 
Property / Symbols used: Q11920 / rank
 
Normal rank
Property / Symbols used: Q11920 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q11920 / qualifier
 
xml-id: C19.S30.XMD6.m1adec

Latest revision as of 14:23, 2 January 2020

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DLMF:19.30.E12
No description defined

    Statements

    Defining formula
    s = a ⁢ F ⁡ ( ϕ , 1 / 2 ) , 𝑠 𝑎 elliptic-integral-first-kind-F italic-ϕ 1 2 {\displaystyle{\displaystyle s=aF\left(\phi,1/\sqrt{2}\right),}}
    0 references
    DLMF id
    DLMF:19.30.E12
    0 references
    constraint
    ϕ = arcsin ⁡ 2 / ( q + 1 ) = arccos ⁡ ( tan ⁡ θ ) italic-ϕ 2 𝑞 1 𝜃 {\displaystyle{\displaystyle\phi=\operatorname{arcsin}\sqrt{2/(q+1)}=% \operatorname{arccos}\left(\tan\theta\right)}}
    0 references
    Symbols used
    Legendre’s incomplete elliptic integral of the first kind
    Defining formula
    F ⁡ ( ϕ , k ) elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}
    xml-id
    C19.S2.E4.m2aadec
    0 references
    Q11208
    Defining formula
    arccos ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m6adec
    0 references
    Q11242
    Defining formula
    arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5adec
    0 references
    tangent function
    Defining formula
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2adec
    0 references
    Q11807
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1edec
    0 references
    Q11919
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C19.S30.XMD5.m1adec
    0 references
    Q11920
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C19.S30.XMD6.m1adec
    0 references
     
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