About the Project

Cosines

AdvancedHelp

(0.002 seconds)

1—10 of 287 matching pages

1: 8.21 Generalized Sine and Cosine Integrals
§8.21 Generalized Sine and Cosine Integrals
§8.21(iv) Interrelations
§8.21(v) Special Values
§8.21(viii) Asymptotic Expansions
2: 6.2 Definitions and Interrelations
§6.2(ii) Sine and Cosine Integrals
Values at Infinity
Hyperbolic Analogs of the Sine and Cosine Integrals
§6.2(iii) Auxiliary Functions
3: 4.21 Identities
4.21.8 cos u + cos v = 2 cos ( u + v 2 ) cos ( u v 2 ) ,
4.21.16 2 cos u cos v = cos ( u v ) + cos ( u + v ) ,
4.21.25 cos ( z ) = cos z ,
4.21.31 cos ( 3 z ) = 3 cos z + 4 cos 3 z ,
4.21.33 cos ( 4 z ) = 8 cos 4 z 8 cos 2 z + 1 .
4: 4.35 Identities
4.35.7 cosh u + cosh v = 2 cosh ( u + v 2 ) cosh ( u v 2 ) ,
4.35.15 2 cosh u cosh v = cosh ( u + v ) + cosh ( u v ) ,
4.35.24 cosh ( z ) = cosh z ,
4.35.30 cosh ( 3 z ) = 3 cosh z + 4 cosh 3 z ,
4.35.35 cosh z = cosh x cos y + i sinh x sin y ,
5: 6.17 Physical Applications
§6.17 Physical Applications
Lebedev (1965) gives an application to electromagnetic theory (radiation of a linear half-wave oscillator), in which sine and cosine integrals are used.
6: 4.42 Solution of Triangles
4.42.5 c 2 = a 2 + b 2 2 a b cos C ,
4.42.6 a = b cos C + c cos B
4.42.8 cos a = cos b cos c + sin b sin c cos A ,
4.42.10 sin a cos B = cos b sin c sin b cos c cos A ,
4.42.12 cos A = cos B cos C + sin B sin C cos a .
7: 6.1 Special Notation
Unless otherwise noted, primes indicate derivatives with respect to the argument. The main functions treated in this chapter are the exponential integrals Ei ( x ) , E 1 ( z ) , and Ein ( z ) ; the logarithmic integral li ( x ) ; the sine integrals Si ( z ) and si ( z ) ; the cosine integrals Ci ( z ) and Cin ( z ) .
8: 6.4 Analytic Continuation
§6.4 Analytic Continuation
6.4.4 Ci ( z e ± π i ) = ± π i + Ci ( z ) ,
6.4.7 g ( z e ± π i ) = π i e i z + g ( z ) .
Unless indicated otherwise, in the rest of this chapter and elsewhere in the DLMF the functions E 1 ( z ) , Ci ( z ) , Chi ( z ) , f ( z ) , and g ( z ) assume their principal values, that is, the branches that are real on the positive real axis and two-valued on the negative real axis.
9: 4.14 Definitions and Periodicity
4.14.2 cos z = e i z + e i z 2 ,
4.14.6 sec z = 1 cos z ,
The functions sin z and cos z are entire. In the zeros of sin z are z = k π , k ; the zeros of cos z are z = ( k + 1 2 ) π , k . …
4.14.9 cos ( z + 2 k π ) = cos z ,
10: 4.32 Inequalities
4.32.1 cosh x ( sinh x x ) 3 ,
4.32.2 sin x cos x < tanh x < x , x > 0 ,
4.32.3 | cosh x cosh y | | x y | sinh x sinh y , x > 0 , y > 0 ,