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Abstract Let k and n be integers with 0 ≤ k ≤ n and p ∈ ( 0 , 1 ) . We prove that the function G ( a… Click to show full abstract
Abstract Let k and n be integers with 0 ≤ k ≤ n and p ∈ ( 0 , 1 ) . We prove that the function G ( a ) = G k , n , p ( a ) = Γ ( a n + 1 ) Γ ( a k + 1 ) Γ ( a ( n − k ) + 1 ) p a k ( 1 − p ) a ( n − k ) is completely monotonic on ( 0 , ∞ ) . This extends a result of Leblanc and Johnson, who showed in 2007 that the sequence { G ( j ) } j = 1 ∞ is decreasing.
Keywords:
complete monotonicity;
monotonicity function;
binomial probability;
function;
function related;
related binomial
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!