About the Project

on critical line or strip

AdvancedHelp

(0.002 seconds)

11—20 of 27 matching pages

11: 4.3 Graphics
Figure 4.3.2 illustrates the conformal mapping of the strip π < z < π onto the whole w -plane cut along the negative real axis, where w = e z and z = ln w (principal value). …
12: 28.29 Definitions and Basic Properties
Q ( z ) is either a continuous and real-valued function for z or an analytic function of z in a doubly-infinite open strip that contains the real axis. … For further results, especially when Q ( z ) is analytic in a strip, see Weinstein and Keller (1987).
13: Bibliography V
  • J. van de Lune, H. J. J. te Riele, and D. T. Winter (1986) On the zeros of the Riemann zeta function in the critical strip. IV. Math. Comp. 46 (174), pp. 667–681.
  • 14: 4.15 Graphics
    Figure 4.15.7 illustrates the conformal mapping of the strip 1 2 π < z < 1 2 π onto the whole w -plane cut along the real axis from to 1 and 1 to , where w = sin z and z = arcsin w (principal value). …
    15: 2.5 Mellin Transform Methods
    The domain of analyticity of f ( z ) is usually an infinite strip a < z < b parallel to the imaginary axis. … If f ( 1 z ) and h ( z ) have a common strip of analyticity a < z < b , then … The sum in (2.5.6) is taken over all poles of x z f ( 1 z ) h ( z ) in the strip d < z < c , and it provides the asymptotic expansion of I ( x ) for small values of x . … To apply the Mellin transform method outlined in §2.5(i), we require the transforms f ( 1 z ) and h ( z ) to have a common strip of analyticity. …
    16: 28.8 Asymptotic Expansions for Large q
    They are uniform with respect to a when 2 q a ( 2 δ ) q , where δ is an arbitrary constant such that 0 < δ < 4 , and also with respect to z in the semi-infinite strip given by 0 z π and z 0 . …
    17: 1.5 Calculus of Two or More Variables
    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 ) . …
    18: 2.10 Sums and Sequences
  • (a)

    On the strip a z n , f ( z ) is analytic in its interior, f ( 2 m ) ( z ) is continuous on its closure, and f ( z ) = o ( e 2 π | z | ) as z ± , uniformly with respect to z [ a , n ] .

  • 19: 28.28 Integrals, Integral Representations, and Integral Equations
    In particular, when h > 0 the integrals (28.28.11), (28.28.14) converge absolutely and uniformly in the half strip z 0 , 0 z π . …
    20: 1.14 Integral Transforms
    If x σ 1 f ( x ) is integrable on ( 0 , ) for all σ in a < σ < b , then the integral (1.14.32) converges and f ( s ) is an analytic function of s in the vertical strip a < s < b . …