DLMF:15.13.E1 (Q5175)

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DLMF:15.13.E1
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    Statements

    Defining formula
    N ⁢ ( a , b , c ) = { 0 , a > 0 , ⌊ - a ⌋ + 1 2 ⁢ ( 1 + S ) , a < 0 , c - a > 0 , ⌊ - a ⌋ + 1 2 ⁢ ( 1 + S ) + ⌊ a - c + 1 ⌋ ⁢ S , a < 0 , c - a < 0 , 𝑁 𝑎 𝑏 𝑐 cases 0 𝑎 0 𝑎 1 2 1 𝑆 formulae-sequence 𝑎 0 𝑐 𝑎 0 𝑎 1 2 1 𝑆 𝑎 𝑐 1 𝑆 formulae-sequence 𝑎 0 𝑐 𝑎 0 {\displaystyle{\displaystyle N(a,b,c)=\begin{cases}0,&a>0,\\ \left\lfloor-a\right\rfloor+\tfrac{1}{2}(1+S),&a<0,c-a>0,\\ \left\lfloor-a\right\rfloor+\tfrac{1}{2}(1+S)+\left\lfloor a-c+1\right\rfloor S% ,&a<0,c-a<0,\\ \end{cases}}}
    0 references
    DLMF id
    DLMF:15.13.E1
    0 references
    Symbols used
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1dec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1dec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1dec
    0 references
    Q11687
    Defining formula
    N ⁢ ( a , b , c ) 𝑁 𝑎 𝑏 𝑐 {\displaystyle{\displaystyle N(a,b,c)}}
    xml-id
    C15.S13.XMD1.m1dec
    0 references
    Q11688
    Defining formula
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C15.S13.XMD2.m1dec
    0 references
     
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