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AiryBi

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

AiryBi[z]
    gives the Airy function Bi(z), the solution of y'' = z y that grows
    exponentially as z -> +Infinity.
AiryBi[0] = 1/(3^(1/6) Gamma[2/3]), AiryBi[Infinity] = Infinity,
AiryBi[-Infinity] = 0. An entire function of z. Real and complex inputs
evaluate numerically at machine or arbitrary (MPFR) precision;
D[AiryBi[z], z] = AiryBiPrime[z]. Listable.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= AiryBi[0]
Out[1]= 1/(3^(1/6) Gamma[2/3])

In[2]:= AiryBi[1.8]
Out[2]= 2.59587

Implementation notes

Attributes: Listable, NumericFunction, Protected, ReadProtected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= AiryBi[0]
Out[1]= 1/(3^(1/6) Gamma[2/3])

In[1]:= N[AiryBi[0], 40]
Out[1]= 0.6149266274460007351509223690936135535947

In[1]:= D[AiryBi[z], z]
Out[1]= AiryBiPrime[z]

In[1]:= N[AiryBi[2.0 + 1.0 I], 20]
Out[1]= 0.778230383757041677129 + 2.50509630006410244363*I

Notes

AiryBi[z] is the dominant solution of the Airy equation y'' == z y, growing exponentially as z -> +Infinity while AiryBi[-Infinity] == 0. Its exact value at the origin is 1/(3^(1/6) Gamma[2/3]), and D[AiryBi[z], z] returns AiryBiPrime[z]. Complex arguments are evaluated to the requested MPFR precision; AiryBi is Listable.