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11: 5.12 Beta Function
12: 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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13: 14.20 Conical (or Mehler) Functions
§14.20 Conical (or Mehler) Functions
►§14.20(i) Definitions and Wronskians
… ► … ►§14.20(ii) Graphics
… ►§14.20(x) Zeros and Integrals
…14: 10.1 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 Bessel functions
, ; Hankel functions
, ; modified Bessel functions
, ; spherical Bessel functions
, , , ; modified spherical Bessel functions
, , ; Kelvin functions
, , , .
For the spherical Bessel functions and modified spherical Bessel functions the order is a nonnegative integer.
…For the Kelvin functions the order is always assumed to be real.
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►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
15: 4.2 Definitions
16: 8.17 Incomplete Beta Functions
§8.17 Incomplete Beta Functions
… ►§8.17(ii) Hypergeometric Representations
… ►For the hypergeometric function see §15.2(i). ►§8.17(iii) Integral Representation
… ►§8.17(vi) Sums
…17: 16.2 Definition and Analytic Properties
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§16.2(i) Generalized Hypergeometric Series
… ►Equivalently, the function is denoted by or , and sometimes, for brevity, by . … ► … ►§16.2(v) Behavior with Respect to Parameters
… ►When and is fixed and not a branch point, any branch of is an entire function of each of the parameters .18: 1.10 Functions of a Complex Variable
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§1.10(vi) Multivalued Functions
… ►Let be a multivalued function and be a domain. … ►The function is many-valued with branch points at . … ►§1.10(xi) Generating Functions
… ►Then is the generating function for the functions , which will automatically have an integral representation …19: 17.1 Special Notation
§17.1 Special Notation
… ►nonnegative integers. | |
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