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1: 32.1 Special Notation
m , n integers.
x real variable.
z complex variable.
2: 9.14 Incomplete Airy Functions
Incomplete Airy functions are defined by the contour integral (9.5.4) when one of the integration limits is replaced by a variable real or complex parameter. …
3: 4.32 Inequalities
4.32.1 cosh x ( sinh x x ) 3 ,
4.32.2 sin x cos x < tanh x < x , x > 0 ,
4.32.3 | cosh x cosh y | | x y | sinh x sinh y , x > 0 , y > 0 ,
4.32.4 arctan x 1 2 π tanh x , x 0 .
4: 10.76 Approximations
Real Variable and Order : Functions
Real Variable and Order : Zeros
Real Variable and Order : Integrals
Complex Variable; Real Order
Real Variable; Imaginary Order
5: 12.3 Graphics
§12.3(i) Real Variables
See accompanying text
Figure 12.3.8: V ( a , x ) , 2.5 a 2.5 , 2.5 x 2.5 . Magnify 3D Help
6: 4.15 Graphics
4.15.1 cos ( x + i y ) = sin ( x + 1 2 π + i y ) ,
4.15.2 cot ( x + i y ) = tan ( x + 1 2 π + i y ) ,
7: 28.30 Expansions in Series of Eigenfunctions
§28.30(i) Real Variable
28.30.1 w m ′′ + ( λ ^ m + Q ( x ) ) w m = 0 ,
28.30.3 f ( x ) = m = 0 f m w m ( x ) ,
28.30.4 f m = 1 2 π 0 2 π f ( x ) w m ( x ) d x .
8: 5.3 Graphics
§5.3(i) Real Argument
9: 12.13 Sums
12.13.1 U ( a , x + y ) = e 1 2 x y + 1 4 y 2 m = 0 ( y ) m m ! U ( a m , x ) ,
12.13.2 U ( a , x + y ) = e 1 2 x y 1 4 y 2 m = 0 ( a 1 2 m ) y m U ( a + m , x ) ,
12.13.3 V ( a , x + y ) = e 1 2 x y + 1 4 y 2 m = 0 ( a 1 2 m ) y m V ( a m , x ) ,
12.13.4 V ( a , x + y ) = e 1 2 x y 1 4 y 2 m = 0 y m m ! V ( a + m , x ) .
12.13.5 U ( a , x cos t + y sin t ) = e 1 4 ( x sin t y cos t ) 2 m = 0 ( a 1 2 m ) ( tan t ) m U ( m + a , x ) U ( m 1 2 , y ) , a 1 2 , 0 t 1 4 π .
10: 6.1 Special Notation
x real variable.