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The powers of {{mvar|z}} are taken using {{math|−3''π''/2 < arg ''z'' ≤ ''π''/2}}.<ref> This is derived from Abramowitz and Stegun (see reference below), [http://people.math.sfu.ca/~cbm/aands/page_508.htm page 508], where a full asymptotic series is given. They switch the sign of the exponent in {{math|exp(''iπa'')}} in the right half-plane but this is immaterial, as the term is negligible there or else {{mvar|a}} is an integer and the sign doesn't matter.</ref> The first term is not needed when {{math|Γ(''b'' − ''a'')}} is finite, that is when {{math|''b'' − ''a''}} is not a non-positive integer and the real part of {{mvar|z}} goes to negative infinity, whereas the second term is not needed when {{math|Γ(''a'')}} is finite, that is, when {{mvar|a}} is a not a non-positive integer and the real part of {{mvar|z}} goes to positive infinity.
There is always some solution to Kummer's equation asymptotic to {{math|''e<sup>z</sup>z''
==Relations==
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