Gauss hypergeometric functions

doctorcj

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Is it possible to write simple expressions for the Gauss hypergeometric functions F(1,15/8,23/8;z)
and F(1,1/8,9/8,z)
 
Is it possible to write simple expressions for the Gauss hypergeometric functions F(1,15/8,23/8;z)
and F(1,1/8,9/8,z)

Exactly how simple is simple? Simplicity is in the eye of the beholder!

For systematic lists of some of the many thousands of published identities involving the hypergeometric function, see the reference works by Arthur Erdélyi, Wilhelm Magnus, and Fritz Oberhettinger et al. (1953), Abramowitz & Stegun (1965), and Daalhuis (2010).(from Wiki)
 
Gauss hypergeometric

Exactly how simple is simple? Simplicity is in the eye of the beholder!

For systematic lists of some of the many thousands of published identities involving the hypergeometric function, see the reference works by Arthur Erdélyi, Wilhelm Magnus, and Fritz Oberhettinger et al. (1953), Abramowitz & Stegun (1965), and Daalhuis (2010).(from Wiki)

The search in Wolfram handbook or Slater's book does not yield a closed form expression whereas the result seems to be a binomial expansion such as (1-z)^(p/q)for both the Gauss hypergeometric functions.The use of well -known identities does not result in the expected result!
 
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