Sentence examples for function of the first order from inspiring English sources

We then obtain, (10) where J1 is a Bessel function of the first order.

where ρ ( y ) = y − [ y ] − 1 2 is the Bernoulli function of the first order.

where ρ ( y ) = y − [ y ] − 1 2 is a Bernoulli function of the first order.

where E 1 ( z ) = ∫ z ∞ e − t t dt (24). is the exponential integral function of the first order [25].

Note that, according to the condition of Theorem 5.1, the Cauchy function of the first order equation (5.3) is positive for 0 ≤ s ≤ t ≤ + ∞.

where we set p 2 i ( s ) = 0 for s < 0, implies the positivity of the Cauchy function of the first order equation (5.3) (see Theorem 15.7, p.358 in [28]).

The solution to the Goursat system is related to the solution of a simpler, explicitly solvable Goursat system through a suitable infinite series of powers of partial derivatives which is summed explicitly in terms of special functions, including Bessel functions and the generalized Marcum Q-functions of the first order.

where J 1 and Y 1 are the Bessel functions of the first order.

On the other hand, a performance, along with its physical trappings, falls under the heading of interpretation, commonly held to be a creative function of the second order, though it does not have to be.

The formula of the peak factor is simplified to a function of the third order moment (skewness) considering the spatial correlation of wind velocity, the resonance response and the background response.

where κ is the Rician factor, and I0 represents the modified Bessel function of the zeroth order and first kind.