general values
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11—20 of 180 matching pages
11: 4.8 Identities
12: 16.2 Definition and Analytic Properties
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►Unless indicated otherwise it is assumed that in the DLMF generalized hypergeometric functions assume their principal values.
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►In general the series (16.2.1) diverges for all nonzero values of .
…Note that if is the value of the numerically largest that is a nonpositive integer, then the identity
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13: 33.13 Complex Variable and Parameters
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►The functions , , and may be extended to noninteger values of by generalizing
, and supplementing (33.6.5) by a formula derived from (33.2.8) with expanded via (13.2.42).
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14: 16.4 Argument Unity
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►The function with argument unity and general values of the parameters is discussed in Bühring (1992).
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15: 22.15 Inverse Functions
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►The principal values satisfy
…and unless stated otherwise it is assumed that the inverse functions assume their principal values.
The general solutions of (22.15.1), (22.15.2), (22.15.3) are, respectively,
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16: 1.9 Calculus of a Complex Variable
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►Equations (1.9.18) and (1.9.20) hold for general values of the phases, but not necessarily for the principal values.
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17: 35.8 Generalized Hypergeometric Functions of Matrix Argument
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Value at
…18: 12.14 The Function
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►These follow from the contour integrals of §12.5(ii), which are valid for general complex values of the argument and parameter .
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