[1−1]
とおく.a(0,∞)に対し, 43 のαにおける微分商を
と表し,
$3[a] (s) =
P3(y) = [1³] ¹ (y) = (€ (0,0)) for y € (0,00)
C3 =
=
(2)
Q[Y3; α] (s) = (43(a+s) — 43 (a)) for s € (-a, ∞)\ {0}
8
43(a+s) +243 (α)
343(a)² (43(a+s)² +43(α) 43 (α + 8) +43(α)²)²
2 (43(3)+243(2))
3 (43(2)² +43(2) + 1)²
が成り立つことを用いてよい.
(1)
とおくとき、次を示せ.但し, 43: (0,∞) R が (0,∞) 上で単調増加であること、及び,
P3(1) = 1, 43(y)³ = y, 43(y) = 43(ÿ) 43(Y), 3( 43(ỹ)
403 (4)
for y,ỹ € (0,00)
43(y)
(€ (0,00))
1
343(a)²
for 8 € (-a, 00),
=
(43(a+s) - 43(a)) (43(a+8)² +43(a) 43 (a + 8) +43(a)²) =
= S
for 8 € (-a, ∞o).
-
- Q[3;a] (s) = P3[a] (s)s for s E (-a, ∞)\{0}.
