Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 31/Special Cases

Hypergeometric Functions
$31.3$: Power of One plus x in terms of Gaussian Hypergeometric Function

$31.4$: Logarithm of One plus x in terms of Gaussian Hypergeometric Function

$31.5$: Exponential Function as Limit of Gaussian Hypergeometric Function

$31.6$: Cosine Function in terms of Gaussian Hypergeometric Function

$31.7$: Secant Function in terms of Gaussian Hypergeometric Function

$31.8$: Arcsine Function in terms of Gaussian Hypergeometric Function

$31.9$: Arctangent Function in terms of Gaussian Hypergeometric Function

$31.10$: Reciprocal of One minus x in terms of Gaussian Hypergeometric Function

$31.11$: Legendre Polynomial in terms of Gaussian Hypergeometric Function

$31.12$: Chebyshev Polynomial of First Kind in terms of Gaussian Hypergeometric Function