DLMF:30.15.E3 (Q8945)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:30.15.E3
No description defined

    Statements

    Defining formula
    ∫ - τ τ sin ⁡ σ ⁢ ( t - s ) π ⁢ ( t - s ) ⁢ ϕ n ⁢ ( s ) ⁢ d s = Λ n ⁢ ϕ n ⁢ ( t ) . superscript subscript 𝜏 𝜏 𝜎 𝑡 𝑠 𝜋 𝑡 𝑠 subscript italic-ϕ 𝑛 𝑠 𝑠 subscript Λ 𝑛 subscript italic-ϕ 𝑛 𝑡 {\displaystyle{\displaystyle\int_{-\tau}^{\tau}\frac{\sin\sigma(t-s)}{\pi(t-s)% }\phi_{n}(s)\mathrm{d}s=\Lambda_{n}\phi_{n}(t).}}
    0 references
    DLMF id
    DLMF:30.15.E3
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1bdec
    0 references
    Q12451
    Defining formula
    τ > 0 𝜏 0 {\displaystyle{\displaystyle\tau>0}}
    xml-id
    C30.S15.XMD1.m1adec
    0 references
    Q12452
    Defining formula
    σ > 0 𝜎 0 {\displaystyle{\displaystyle\sigma>0}}
    xml-id
    C30.S15.XMD2.m1dec
    0 references
    function (locally)
    Defining formula
    ϕ n ⁢ ( t ) subscript italic-ϕ 𝑛 𝑡 {\displaystyle{\displaystyle\phi_{n}(t)}}
    xml-id
    C30.S15.XMD3.m1adec
    0 references
    DLMF:30.15.E2
    Defining formula
    Λ Λ {\displaystyle{\displaystyle\Lambda}}
    xml-id
    C30.S15.XMD4.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8945&oldid=35951"