Harman Patil (Editor)

Ferrers function

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In mathematics, Ferrers functions are defined in terms of hypergeometric functions They are named after Norman Macleod Ferrers.

Ferrers function of the first kind
P v μ ( x ) = ( 1 + x 1 − x ) μ / 2 ⋅ F ( v + 1 , − v ; 1 − μ ; 1 / 2 − x / 2 ) Γ ( 1 − μ )
Ferrers function of the second kind
Q v μ ( x ) = cos ⁡ ( μ π ) ( 1 + x 1 − x ) μ / 2 F ( v + 1 , − v ; 1 − μ ; 1 / 2 − 2 / x ) Γ ( 1 − μ )

References

Ferrers function Wikipedia
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