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Showing content from https://dlmf.nist.gov/4.19 below:

§4.19 Maclaurin Series and Laurent Series ‣ Trigonometric Functions ‣ Chapter 4 Elementary Functions

Keywords:

Laurent series, Maclaurin series, trigonometric functions

Notes:

See Hobson (1928, pp. 288–293, 360–367).

Referenced by:

§24.2(i)

Permalink:

http://dlmf.nist.gov/4.19

See also:

Annotations for Ch.4

Symbols:

! : factorial (as in n ! ), sin ⁡ z : sine function and z : complex variable

A&S Ref:

4.3.65

Referenced by:

§4.45(i)

Permalink:

http://dlmf.nist.gov/4.19.E1

Encodings:

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See also:

Annotations for §4.19 and Ch.4

Symbols:

cos ⁡ z : cosine function, ! : factorial (as in n ! ) and z : complex variable

A&S Ref:

4.3.66

Referenced by:

§4.45(i)

Permalink:

http://dlmf.nist.gov/4.19.E2

Encodings:

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See also:

Annotations for §4.19 and Ch.4

In (4.19.3)–(4.19.9), B n are the Bernoulli numbers and E n are the Euler numbers (§§24.2(i)–24.2(ii)).

Symbols:

B n : Bernoulli numbers, π : the ratio of the circumference of a circle to its diameter, ! : factorial (as in n ! ), tan ⁡ z : tangent function, n : integer and z : complex variable

A&S Ref:

4.3.67

Referenced by:

§4.19

Permalink:

http://dlmf.nist.gov/4.19.E3

Encodings:

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See also:

Annotations for §4.19 and Ch.4

Symbols:

B n : Bernoulli numbers, π : the ratio of the circumference of a circle to its diameter, csc ⁡ z : cosecant function, ! : factorial (as in n ! ), n : integer and z : complex variable

A&S Ref:

4.3.68

Referenced by:

§4.33

Permalink:

http://dlmf.nist.gov/4.19.E4

Encodings:

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See also:

Annotations for §4.19 and Ch.4

Symbols:

E n : Euler numbers, π : the ratio of the circumference of a circle to its diameter, ! : factorial (as in n ! ), sec ⁡ z : secant function, n : integer and z : complex variable

A&S Ref:

4.3.69

Referenced by:

§24.1, §24.19(i), §24.2(ii)

Permalink:

http://dlmf.nist.gov/4.19.E5

Encodings:

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See also:

Annotations for §4.19 and Ch.4

Symbols:

B n : Bernoulli numbers, π : the ratio of the circumference of a circle to its diameter, cot ⁡ z : cotangent function, ! : factorial (as in n ! ), n : integer and z : complex variable

A&S Ref:

4.3.70

Permalink:

http://dlmf.nist.gov/4.19.E6

Encodings:

TeX, pMML, png

See also:

Annotations for §4.19 and Ch.4

Symbols:

B n : Bernoulli numbers, π : the ratio of the circumference of a circle to its diameter, ! : factorial (as in n ! ), ln ⁡ z : principal branch of logarithm function, sin ⁡ z : sine function, n : integer and z : complex variable

A&S Ref:

4.3.71

Permalink:

http://dlmf.nist.gov/4.19.E7

Encodings:

TeX, pMML, png

See also:

Annotations for §4.19 and Ch.4

Symbols:

B n : Bernoulli numbers, π : the ratio of the circumference of a circle to its diameter, cos ⁡ z : cosine function, ! : factorial (as in n ! ), ln ⁡ z : principal branch of logarithm function, n : integer and z : complex variable

A&S Ref:

4.3.72

Permalink:

http://dlmf.nist.gov/4.19.E8

Encodings:

TeX, pMML, png

See also:

Annotations for §4.19 and Ch.4

Symbols:

B n : Bernoulli numbers, π : the ratio of the circumference of a circle to its diameter, ! : factorial (as in n ! ), ln ⁡ z : principal branch of logarithm function, tan ⁡ z : tangent function, n : integer and z : complex variable

A&S Ref:

4.3.73

Referenced by:

§4.19, §4.33

Permalink:

http://dlmf.nist.gov/4.19.E9

Encodings:

TeX, pMML, png

See also:

Annotations for §4.19 and Ch.4

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