(For other notation see Notation for the Special Functions.)
|, ,||real variables.|
|,||nonnegative integers used for order and degree, respectively.|
|,||general order and degree, respectively.|
|complex degree, .|
|Euler’s constant (§5.2(ii)).|
|arbitrary small positive constant.|
|logarithmic derivative of gamma function (§5.2(i)).|
|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).