In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the...

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that...

In mathematics, the method of matched asymptotic expansions is a common approach to finding an accurate approximation to the solution to an equation,...

this asymptotic expansion are needed to obtain a good approximation of erfc x (while for not too large values of x, the above Taylor expansion at 0 provides...

and only large values of x are employed. This expansion follows directly from the asymptotic expansion for the exponential integral. This implies e.g...

In mathematics, the polygamma function of order m is a meromorphic function on the complex numbers C {\displaystyle \mathbb {C} } defined as the (m + 1)th...

the digamma function A product formula for the gamma function The asymptotic expansion of the gamma function for small arguments. An inequality for Euler's...

\mathbb {C} } and z ∈ Ω a {\displaystyle z\in \Omega _{a}} , an asymptotic expansion of Φ ( z , s , a ) {\displaystyle \Phi (z,s,a)} for large a {\displaystyle...

integral representation can be manipulated to give the start of the asymptotic expansion of ψ {\displaystyle \psi } . ψ ( z ) = log ⁡ z − 1 2 z − ∫ 0 ∞ (...

_{-\infty }^{\infty }(x+iy)^{n}e^{-{\frac {y^{2}}{2}}}\,dy.} Asymptotically, as n → ∞, the expansion e − x 2 2 ⋅ H n ( x ) ∼ 2 n π Γ ( n + 1 2 ) cos ⁡ ( x 2...