DLMF:22.16.E31 (Q7151)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:22.16.E31
No description defined

    Statements

    Defining formula
    E ⁑ ( am ⁑ ( x , k ) , k ) = β„° ⁑ ( x , k ) , elliptic-integral-second-kind-E Jacobi-elliptic-amplitude π‘₯ π‘˜ π‘˜ Jacobi-Epsilon π‘₯ π‘˜ {\displaystyle{\displaystyle E\left(\operatorname{am}\left(x,k\right),k\right)% =\mathcal{E}\left(x,k\right),}}
    0 references
    DLMF id
    DLMF:22.16.E31
    0 references
    constraint
    - K ≀ x ≀ K 𝐾 π‘₯ 𝐾 {\displaystyle{\displaystyle-K\leq x\leq K}}
    0 references
    Symbols used
    Jacobi’s epsilon function
    Defining formula
    β„° ⁑ ( x , k ) Jacobi-Epsilon π‘₯ π‘˜ {\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S16.E14.m2aqdec
    0 references
    Jacobi’s amplitude function
    Defining formula
    am ⁑ ( x , k ) Jacobi-elliptic-amplitude π‘₯ π‘˜ {\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S16.E1.m2aldec
    0 references
    Q11600
    Defining formula
    K ⁑ ( k ) complete-elliptic-integral-first-kind-K π‘˜ {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1aedec
    0 references
    Legendre’s incomplete elliptic integral of the second kind
    Defining formula
    E ⁑ ( Ο• , k ) elliptic-integral-second-kind-E italic-Ο• π‘˜ {\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}
    xml-id
    C19.S2.E5.m2adec
    0 references
    Q12003
    Defining formula
    x π‘₯ {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1addec
    0 references
    Q11984
    Defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1abdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7151&oldid=59336"