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Symbolic formulas for Airy equations?

I can find the Airy formula's in Mathematica under the author's name. Ai and Bi. I do not care to work with the formula's as named expressions. I would prefer to work with symbols, like Cosine and the Integral and so forth and so on. How do I convert these named expressions to symbolic relations?
POSTED BY: Alan White
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Thank you sir. Thanks very much.
POSTED BY: Alan White

See: here

For example Integral representations AiryAi[z] is :

AiryAi[z] == (1/Pi) Integrate[Cos[t^3/3 + z t], {t, 0, Infinity}] /; Im[z] == 0

Or use this commands:

MathematicalFunctionData["AiryAi", "SeriesRepresentations"]
MathematicalFunctionData["AiryAi", "IntegralRepresentations"]
MathematicalFunctionData["AiryAi", "LimitRepresentations"]
MathematicalFunctionData["AiryAi", "AlternativeRepresentations"]

Regards M.I.
POSTED BY: Mariusz Iwaniuk

Thanks very much Professor Iwaniuk. Your answer is very comprehensive but not exactly what I need. I thought there was a command in Mathematica converting each and every named equation (Like: Binomial[n, p]) to an algebraic format. Worse, I am not able to Plot the integral form of the AiryAi expression in the first line of your response. This is my fault. I am not enough of a programmer to understand the meaning of symbols like: /; and Im[z] == 0. Thanks again.

POSTED BY: Alan White
POSTED BY: Mariusz Iwaniuk
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