About the Project
NIST

differentiable

AdvancedHelp

(0.001 seconds)

1—10 of 29 matching pages

1: 18.32 OP’s with Respect to Freud Weights
where Q ( x ) is real, even, nonnegative, and continuously differentiable. …
2: 1.4 Calculus of One Variable
When this limit exists f is differentiable at x . … When n 1 , f is continuously differentiable on I . … …
Mean Value Theorem
A continuously differentiable function is convex iff the curve does not lie below its tangent at any point. …
3: 1.6 Vectors and Vector-Valued Functions
when f is continuously differentiable. … The curve C is piecewise differentiable if c is piecewise differentiable. … … For x , y , and z continuously differentiable, the vectors … For f and g twice-continuously differentiable functions …
4: 4.12 Generalized Logarithms and Exponentials
Both ϕ ( x ) and ψ ( x ) are continuously differentiable. … For C generalized logarithms, see Walker (1991). …
5: 2.3 Integrals of a Real Variable
converges for all sufficiently large x , and q ( t ) is infinitely differentiable in a neighborhood of the origin. … If, in addition, q ( t ) is infinitely differentiable on [ 0 , ) and … assume a and b are finite, and q ( t ) is infinitely differentiable on [ a , b ] . … Assume that q ( t ) again has the expansion (2.3.7) and this expansion is infinitely differentiable, q ( t ) is infinitely differentiable on ( 0 , ) , and each of the integrals e i x t q ( s ) ( t ) d t , s = 0 , 1 , 2 , , converges at t = , uniformly for all sufficiently large x . …
  • (a)

    On ( a , b ) , p ( t ) and q ( t ) are infinitely differentiable and p ( t ) > 0 .

  • 6: 1.13 Differential Equations
    Let W ( z ) satisfy (1.13.14), ζ ( z ) be any thrice-differentiable function of z , and
    1.13.18 U ( z ) = ( ζ ( z ) ) 1 / 2 W ( z ) .
    1.13.19 d 2 U d ζ 2 = ( z ˙ 2 H ( z ) - 1 2 { z , ζ } ) U .
    1.13.21 { z , ζ } = ( d ξ / d ζ ) 2 { z , ξ } + { ξ , ζ } .
    1.13.22 { z , ζ } = - ( d z / d ζ ) 2 { ζ , z } .
    7: 2.8 Differential Equations with a Parameter
    The expansions (2.8.11) and (2.8.12) are both uniform and differentiable with respect to ξ . … Again, u > 0 and ψ ( ξ ) is C on ( α 1 , α 2 ) . … The expansions (2.8.15) and (2.8.16) are both uniform and differentiable with respect to ξ . … The expansions (2.8.25) and (2.8.26) are both uniform and differentiable with respect to ξ . … The expansions (2.8.29) and (2.8.30) are both uniform and differentiable with respect to ξ . …
    8: 18.38 Mathematical Applications
    In consequence, expansions of functions that are infinitely differentiable on [ - 1 , 1 ] in series of Chebyshev polynomials usually converge extremely rapidly. …
    9: 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. …
    1.5.6 2 f x y = 2 f y x .
    If F ( x , y ) is continuously differentiable, F ( a , b ) = 0 , and F / y 0 at ( a , b ) , then in a neighborhood of ( a , b ) , that is, an open disk centered at a , b , the equation F ( x , y ) = 0 defines a continuously differentiable function y = g ( x ) such that F ( x , g ( x ) ) = 0 , b = g ( a ) , and g ( x ) = - F x / F y . … If f is n + 1 times continuously differentiable, then … Sufficient conditions for validity are: (a) f and f / x are continuous on a rectangle a x b , c y d ; (b) when x [ a , b ] both α ( x ) and β ( x ) are continuously differentiable and lie in [ c , d ] . …
    10: 1.8 Fourier Series
    If a function f ( x ) C 2 [ 0 , 2 π ] is periodic, with period 2 π , then the series obtained by differentiating the Fourier series for f ( x ) term by term converges at every point to f ( x ) . … Suppose that f ( x ) is twice continuously differentiable and f ( x ) and | f ′′ ( x ) | are integrable over ( - , ) . …