# Symbolic formulas for Airy equations?

Posted 1 month ago
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 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?
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Posted 1 month ago
 Thank you sir. Thanks very much.
Posted 1 month ago
 See: hereFor 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 1 month ago
 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 1 month ago
 Binomial[n, p]) to an algebraic format ?.Probably you want: FullSimplify[Binomial[n, p] // FunctionExpand, Assumptions -> {n, p} \[Element] PositiveIntegers] (*n!/(p! Gamma[1 + n - p])*) AiryAi[z] // FunctionExpand(*Dosen't work ! *) For integral where: Im[z] == 0 that's mean,formula works only for: $z\in \mathbb{R}$You can plot the integral form, see code below: AIR[z_?NumericQ] := (1/Pi) *NIntegrate[Cos[t^3/3 + z t], {t, 0, Infinity}] Plot[{AIR[z], AiryAi[z]}, {z, -2, 2}, PlotStyle -> {Red, {Black, Dashed}}, PlotLegends -> "Expressions"] Regards M.I.