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11: 16.13 Appell Functions
§16.13 Appell Functions
►The following four functions of two real or complex variables and cannot be expressed as a product of two functions, in general, but they satisfy partial differential equations that resemble the hypergeometric differential equation (15.10.1): ►
16.13.1
,
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16.13.4
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12: 5.12 Beta Function
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: 4.2 Definitions
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►The general logarithm function
is defined by
…This is a multivalued function of with branch point at .
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►Most texts extend the definition of the principal value to include the branch cut
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§4.2(iii) The Exponential Function
… ►§4.2(iv) Powers
…15: 10.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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►For the spherical Bessel functions and modified spherical Bessel functions the order is a nonnegative integer.
For the other functions when the order is replaced by , it can be any integer.
For the Kelvin functions the order is always assumed to be real.
…
►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
16: 4.37 Inverse Hyperbolic Functions
§4.37 Inverse Hyperbolic Functions
… ►Each of the six functions is a multivalued function of . and have branch points at ; the other four functions have branch points at . … ►Other Inverse Functions
… ►§4.37(vi) Interrelations
…17: 4.23 Inverse Trigonometric Functions
§4.23 Inverse Trigonometric Functions
… ►Each of the six functions is a multivalued function of . and have branch points at ; the other four functions have branch points at . … ►Other Inverse Functions
… ►§4.23(viii) Gudermannian Function
…18: 1.10 Functions of a Complex Variable
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