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Beal [28] suggests using the above recurrence to shift x to a value greater than 6 and then applying the above expansion with terms above x 14 cut off, which yields "more than enough precision" (at least 12 digits except near the zeroes). As x goes to infinity, ψ(x) gets arbitrarily close to both ln(x − 1 / 2 ) and ln x.
From this follows that for grains greater than 5 mm the Shields parameter gets a constant value of 0,055. The gradient of a river (I) can be determined by Chézy formula: = in which = the coefficiënt of Chézy ( m 1/2 / s ); This is often in the order 50 ( m 1/2 / s ). For a flat bed (i.e. without ripples) C can be approximated with:
0.8–2 MPa 120–290 psi Pressure used in boilers of steam locomotives [citation needed] 1.1 MPa 162 psi Pressure of an average human bite [citation needed] 2.8–8.3 MPa 400–1,200 psi Pressure of carbon dioxide propellant in a paintball gun [64] 5 MPa 700 psi Water pressure of the output of a coin-operated car wash spray nozzle [58] 5 MPa ...
In the figure, Excel is used to find the smallest root of the quadratic equation x 2 + bx + c = 0 for c = 4 and c = 4 × 10 5. The difference between direct evaluation using the quadratic formula and the approximation described above for widely spaced roots is plotted vs. b.
This expresses the polygamma function as the Laplace transform of (−1) m+1 t m / 1 − e −t . It follows from Bernstein's theorem on monotone functions that, for m > 0 and x real and non-negative, (−1) m+1 ψ (m) (x) is a completely monotone function. Setting m = 0 in the
This assumption is commonly made in engineering practice when the Mach number is less than about 0.3. C p {\displaystyle C_{p}} of zero indicates the pressure is the same as the freestream pressure. C p {\displaystyle C_{p}} of one corresponds to the stagnation pressure and indicates a stagnation point .
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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]