About the Project
NIST

maximum modulus

AdvancedHelp

(0.001 seconds)

1—10 of 47 matching pages

1: 1.10 Functions of a Complex Variable
§1.10(v) Maximum-Modulus Principle
Analytic Functions
Harmonic Functions
Schwarz’s Lemma
2: 19.27 Asymptotic Approximations and Expansions
19.27.13 R J ( x , y , z , p ) = 3 2 z p ( ln ( 8 z a + g ) - 2 R C ( 1 , p z ) + O ( ( a z + a p ) ln p a ) ) , max ( x , y ) / min ( z , p ) 0 .
19.27.14 R J ( x , y , z , p ) = 3 y z R C ( x , p ) - 6 y z R G ( 0 , y , z ) + O ( x + 2 p y z ) , max ( x , p ) / min ( y , z ) 0 .
19.27.16 R J ( x , y , z , p ) = ( 3 / x ) R C ( ( h + p ) 2 , 2 ( b + h ) p ) + O ( 1 x 3 / 2 ln x b + h ) , max ( y , z , p ) / x 0 .
3: 16.21 Differential Equation
where again ϑ = z d / d z . This equation is of order max ( p , q ) . …
4: 14.21 Definitions and Basic Properties
The generating function expansions (14.7.19) (with P replaced by P ) and (14.7.22) apply when | h | < min | z ± ( z 2 - 1 ) 1 / 2 | ; (14.7.21) (with P replaced by P ) applies when | h | > max | z ± ( z 2 - 1 ) 1 / 2 | .
5: 13.10 Integrals
13.10.3 0 e - z t t b - 1 M ( a , c , k t ) d t = Γ ( b ) z - b F 1 2 ( a , b ; c ; k / z ) , b > 0 , z > max ( k , 0 ) ,
6: 19.9 Inequalities
19.9.12 max ( sin ϕ , ϕ Δ ) E ( ϕ , k ) ϕ ,
7: Bibliography M
  • A. J. MacLeod (1998) Algorithm 779: Fermi-Dirac functions of order - 1 / 2 , 1 / 2 , 3 / 2 , 5 / 2 . ACM Trans. Math. Software 24 (1), pp. 1–12.
  • 8: 3.2 Linear Algebra
    and back substitution is x n = y n / d n , followed by … The p -norm of a vector x = [ x 1 , , x n ] T is given by …
    x = max 1 j n | x j | .
    3.2.14 A p = max x 0 A x p x p .
    A 1 = max 1 k n j = 1 n | a j k | ,
    9: 6.16 Mathematical Applications
    The first maximum of 1 2 Si ( x ) for positive x occurs at x = π and equals ( 1.1789 ) × 1 4 π ; compare Figure 6.3.2. Hence if x = π / ( 2 n ) and n , then the limiting value of S n ( x ) overshoots 1 4 π by approximately 18%. Similarly if x = π / n , then the limiting value of S n ( x ) undershoots 1 4 π by approximately 10%, and so on. …
    10: 1.5 Calculus of Two or More Variables
    The function f ( x , y ) is continuously differentiable if f , f / x , and f / y are continuous, and twice-continuously differentiable if also 2 f / x 2 , 2 f / y 2 , 2 f / x y , and 2 f / y x are continuous. … where f and its partial derivatives on the right-hand side are evaluated at ( a , b ) , and R n / ( λ 2 + μ 2 ) n / 2 0 as ( λ , μ ) ( 0 , 0 ) . f ( x , y ) has a local minimum (maximum) at ( a , b ) if … Suppose that a , b , c are finite, d is finite or + , and f ( x , y ) , f / x are continuous on the partly-closed rectangle or infinite strip [ a , b ] × [ c , d ) . … as max ( ( x j + 1 - x j ) + ( y k + 1 - y k ) ) 0 . …