§4.32 Inequalities

For real,

4.32.1

Symbols:

: hyperbolic cosine function, : hyperbolic sine function and : real variable

Permalink:

http://dlmf.nist.gov/4.32.E1

Encodings:

TeX, pMML, png

4.32.2,

Symbols:

: cosine function, : hyperbolic tangent function, : sine function and : real variable

Permalink:

http://dlmf.nist.gov/4.32.E2

Encodings:

TeX, pMML, png

4.32.3, ,

Symbols:

: hyperbolic cosine function, : hyperbolic sine function, : real variable and : real variable

Permalink:

http://dlmf.nist.gov/4.32.E3

Encodings:

TeX, pMML, png

4.32.4.

Symbols:

: hyperbolic tangent function, : arctangent function and : real variable

Permalink:

http://dlmf.nist.gov/4.32.E4

Encodings:

TeX, pMML, png

For these and other inequalities involving hyperbolic functions see Mitrinović (1964, pp. 61, 76, 159) and Mitrinović (1970, p. 270).