DLMF:19.30.E12 (Q6687)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:19.30.E12
No description defined

    Statements

    Defining formula
    s = a ⁒ F ⁑ ( Ο• , 1 / 2 ) , 𝑠 π‘Ž elliptic-integral-first-kind-F italic-Ο• 1 2 {\displaystyle{\displaystyle s=aF\left(\phi,1/\sqrt{2}\right),}}
    0 references
    DLMF id
    DLMF:19.30.E12
    0 references
    constraint
    Ο• = arcsin ⁑ 2 / ( q + 1 ) = arccos ⁑ ( tan ⁑ ΞΈ ) italic-Ο• 2 π‘ž 1 πœƒ {\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 ⁑ ( Ο• , k ) elliptic-integral-first-kind-F italic-Ο• π‘˜ {\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
    Ο• italic-Ο• {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1edec
    0 references
    Q11919
    Defining formula
    q π‘ž {\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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6687&oldid=46651"