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R(z0 , ρ) (p. 8)

The set of z with |z| > ρ
R(∞, ρ) (p. 14)

rf (z, N ) The residue term of order N in the asymptotic expansion
of the function f (p. 65)

s± The substitution map (p. 78)

S(d, ±) The sector with bisecting direction d, opening ± and in¬-
nite radius (p. 60)
Symbols 299

S(d, ±, ρ) A sector with bisecting direction d, opening ± and radius
ρ that may be ¬nite or not (p. 60)
¯
S(d, ±, ρ) A closed sector with bisecting direction d, opening ± and
radius ρ (p. 60)
S± Two sectors with bisecting direction 0, resp, π, and open-
ings adding up to 2π (p. 84)
Denotes a general summation method (p. 97)
S

Denotes a matrix summation method (p. 97)
SA
ˆ ˆ
Sk,d (f ) The k-sum of f in direction d (p. 100)
ˆ ˆ
ST,d f The T -sum of f in direction d (p. 108)
ˆ ˆ
ST ,d f The T -sum of f in the multidirection d (p. 161)

Suppj A set of pairs (n, m), for which the jth Stokes multipliers
may have nontrivial blocks (p. 141)

T A tuple of integral operators (p. 161)

T1 — T2 The convolution of integral operators (p. 160)

Z The set of integer numbers

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