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Digital Library of Mathematical Functions ID
2.9.E9
w
j
(
n
)
∼
ρ
n
exp
(
(
-
1
)
j
κ
n
)
n
α
∑
s
=
0
∞
(
-
1
)
j
s
c
s
n
s
/
2
,
asymptotic-expansion
subscript
𝑤
𝑗
𝑛
superscript
𝜌
𝑛
superscript
1
𝑗
𝜅
𝑛
superscript
𝑛
𝛼
superscript
subscript
𝑠
0
superscript
1
𝑗
𝑠
subscript
𝑐
𝑠
superscript
𝑛
𝑠
2
{\displaystyle{\displaystyle w_{j}(n)\sim\rho^{n}\exp\left((-1)^{j}\kappa\sqrt% {n}\right)n^{\alpha}\sum_{s=0}^{\infty}(-1)^{js}\frac{c_{s}}{n^{s/2}},}}
Constraint(s)
Symbols List
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
:
exp
z
𝑧
{\displaystyle{\displaystyle\exp\NVar{z}}}
: exponential function
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
: roots
κ
𝜅
{\displaystyle{\displaystyle\kappa}}
: κ
c
𝑐
{\displaystyle{\displaystyle c}}
: constant
w
j
(
n
)
subscript
𝑤
𝑗
𝑛
{\displaystyle{\displaystyle w_{j}(n)}}
: solutions
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