An asymptotic expansion for the incomplete beta function
An asymptotic expansion for the incomplete beta function
A new asymptotic expansion is derived for the incomplete beta function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I left-parenthesis a comma b comma x right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">I(a,b,x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, which is suitable for large <inline-formula content-type="math/mathml"> <mml:math …