Complete monotonicity of modified Bessel functions
Complete monotonicity of modified Bessel functions
We prove that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="nu greater-than 1 slash 2"> <mml:semantics> <mml:mrow> <mml:mi>ν<!-- ν --></mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\nu > 1/2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2 Superscript nu minus 1 Baseline normal upper Gamma left-parenthesis nu right-parenthesis …