inverse%20Gudermannian%20function
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1: 4.23 Inverse Trigonometric Functions
§4.23 Inverse Trigonometric Functions
►§4.23(i) General Definitions
… ►§4.23(iv) Logarithmic Forms
… ►Other Inverse Functions
… ►The inverse Gudermannian function is given by …2: 4.37 Inverse Hyperbolic Functions
§4.37 Inverse Hyperbolic Functions
►§4.37(i) General Definitions
… ►§4.37(ii) Principal Values
… ►Other Inverse Functions
… ►§4.37(vi) Interrelations
…3: 22.15 Inverse Functions
§22.15 Inverse Functions
►§22.15(i) Definitions
… ►Each of these inverse functions is multivalued. The principal values satisfy … ►4: 14.20 Conical (or Mehler) Functions
§14.20 Conical (or Mehler) Functions
… ► … ►§14.20(ii) Graphics
… ►where the inverse trigonometric functions take their principal values. … ►with the inverse tangent taking its principal value. …5: 9.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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►The main functions treated in this chapter are the Airy functions
and , and the Scorer functions
and (also known as inhomogeneous Airy functions).
►Other notations that have been used are as follows: and for and (Jeffreys (1928), later changed to and ); , (Fock (1945)); (Szegő (1967, §1.81)); , (Tumarkin (1959)).
nonnegative integer, except in §9.9(iii). | |
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6: 31.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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►The main functions treated in this chapter are , , , and the polynomial .
…Sometimes the parameters are suppressed.
, | real variables. |
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7: 23.15 Definitions
§23.15 Definitions
►§23.15(i) General Modular Functions
… ►Elliptic Modular Function
… ►Dedekind’s Eta Function (or Dedekind Modular Function)
… ►8: 5.15 Polygamma Functions
§5.15 Polygamma Functions
►The functions , , are called the polygamma functions. In particular, is the trigamma function; , , are the tetra-, penta-, and hexagamma functions respectively. Most properties of these functions follow straightforwardly by differentiation of properties of the psi function. … ►For see §24.2(i). …9: 5.2 Definitions
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§5.2(i) Gamma and Psi Functions
►Euler’s Integral
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5.2.1
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►It is a meromorphic function with no zeros, and with simple poles of residue at .
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5.2.2
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