DLMF:18.22.E22 (Q5893)

From DRMF
Revision as of 01:37, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:18.22.E22
No description defined

    Statements

    Defining formula
    ∇ x ( ( N x ) ⁢ p x ⁢ ( 1 - p ) N - x ⁢ K n ⁡ ( x ; p , N ) ) = ( N + 1 x ) ⁢ p x ⁢ ( 1 - p ) N - x ⁢ K n + 1 ⁡ ( x ; p , N + 1 ) . backward-difference 𝑥 binomial 𝑁 𝑥 superscript 𝑝 𝑥 superscript 1 𝑝 𝑁 𝑥 Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 binomial 𝑁 1 𝑥 superscript 𝑝 𝑥 superscript 1 𝑝 𝑁 𝑥 Krawtchouk-polynomial-K 𝑛 1 𝑥 𝑝 𝑁 1 {\displaystyle{\displaystyle\nabla_{x}\left(\genfrac{(}{)}{0.0pt}{}{N}{x}p^{x}% (1-p)^{N-x}K_{n}\left(x;p,N\right)\right)=\genfrac{(}{)}{0.0pt}{}{N+1}{x}p^{x}% {(1-p)^{N-x}}K_{n+1}\left(x;p,N+1\right).}}
    0 references
    DLMF id
    DLMF:18.22.E22
    0 references
    Symbols used
    Q11662
    Defining formula
    K n ⁡ ( x ; p , N ) Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 {\displaystyle{\displaystyle K_{\NVar{n}}\left(\NVar{x};\NVar{p},\NVar{N}% \right)}}
    xml-id
    C18.S19.T1.t1.r3.p1.m2acdec
    0 references
    Q11764
    Defining formula
    ∇ x backward-difference 𝑥 {\displaystyle{\displaystyle\nabla_{\NVar{x}}}}
    xml-id
    C18.S1.EGx2.m1aadec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5893&oldid=33079"