TY - JOUR
T1 - Transformation to canonical form for uniform asymptotic expansions
AU - Qu, C. K.
AU - Wong, R.
PY - 1990/6
Y1 - 1990/6
N2 - The existence of a one-to-one analytic transformation z ↔ w is established which takes a function of the form f(z, t) = α(t) z + β(t) logz + z + z2ψ(z, t) into the canonical form f(z, t) = A(t) w + β(t) log w + C(t) + w, where zε{lunate}C and t=(t,t)ε{lunate}C2. The coefficient functions α(t), β(t), A(t), and C(t) are analytic for small |t|, and satisfy α(0) = β(0) = A(0) = C(0) = 0. The function ψ(z, t) is analytic in both z and t for small |z| and |t|. The transformation z ↔ w is frequently needed in uniform asymptotic expansions of integrals. © 1990.
AB - The existence of a one-to-one analytic transformation z ↔ w is established which takes a function of the form f(z, t) = α(t) z + β(t) logz + z + z2ψ(z, t) into the canonical form f(z, t) = A(t) w + β(t) log w + C(t) + w, where zε{lunate}C and t=(t,t)ε{lunate}C2. The coefficient functions α(t), β(t), A(t), and C(t) are analytic for small |t|, and satisfy α(0) = β(0) = A(0) = C(0) = 0. The function ψ(z, t) is analytic in both z and t for small |z| and |t|. The transformation z ↔ w is frequently needed in uniform asymptotic expansions of integrals. © 1990.
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U2 - 10.1016/0022-247X(90)90295-Q
DO - 10.1016/0022-247X(90)90295-Q
M3 - 21_Publication in refereed journal
VL - 149
SP - 210
EP - 219
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -