(For other notation see Notation for the Special Functions.)
, , |
real variables. |
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complex variable. |
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, |
unless stated otherwise, nonnegative integers, used for order and degree, respectively. |
, |
general order and degree, respectively. |
complex degree, . |
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Euler’s constant (§5.2(ii)). |
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arbitrary small positive constant. |
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logarithmic derivative of gamma function (§5.2(i)). |
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. |
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Olver’s scaled hypergeometric function: . |
Multivalued functions take their principal values (§4.2(i)) unless indicated otherwise.
The main functions treated in this chapter are the Legendre functions , , , ; Ferrers functions , (also known as the Legendre functions on the cut); associated Legendre functions , , ; conical functions , , , , (also known as Mehler functions).