AiryBiPrime¶

Status: Stable

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

Description¶

AiryBiPrime[z]
    gives the derivative Bi'(z) of the Airy function AiryBi.
AiryBiPrime[0] = 3^(1/6)/Gamma[1/3], AiryBiPrime[+Infinity] = Infinity. Real
and complex inputs evaluate numerically at machine or arbitrary (MPFR)
precision; D[AiryBiPrime[z], z] = z AiryBi[z]. Listable.

Examples¶

No verified examples yet for this function.

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¶

Source: src/info.c
Specification index: Mathilda_spec.md

Notes & additional examples¶

Worked examples¶

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

In[1]:= N[AiryBiPrime[0], 40]
Out[1]= 0.44828835735382635791482371039882839086616

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

In[1]:= AiryBiPrime[1.0 + 1.0 I]
Out[1]= 0.0756628 + 0.783701*I

Notes¶

AiryBiPrime[z] is the derivative Bi'(z). Its exact origin value is 3^(1/6)/Gamma[1/3], and a further derivative satisfies the Airy equation in the form D[AiryBiPrime[z], z] == z AiryBi[z]. Complex arguments evaluate to machine precision and, under N[..., n], to arbitrary MPFR precision; AiryBiPrime is Listable.