AiryAiPrime¶

Status: Stable

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

Description¶

AiryAiPrime[z]
    gives the derivative Ai'(z) of the Airy function AiryAi.
AiryAiPrime[0] = -1/(3^(1/3) Gamma[1/3]), AiryAiPrime[+Infinity] = 0. Real
and complex inputs evaluate numerically at machine or arbitrary (MPFR)
precision; D[AiryAiPrime[z], z] = z AiryAi[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]:= AiryAiPrime[0]
Out[1]= -1/(3^(1/3) Gamma[1/3])

In[1]:= N[AiryAiPrime[0], 40]
Out[1]= -0.25881940379280679840518356018920396347907

In[1]:= D[AiryAiPrime[z], z]
Out[1]= z AiryAi[z]

In[1]:= AiryAiPrime[1.0 + 1.0 I]
Out[1]= -0.130628 + 0.163068*I

Notes¶

AiryAiPrime[z] is the derivative Ai'(z). Its exact origin value is -1/(3^(1/3) Gamma[1/3]), and differentiating once more recovers the Airy equation in the form D[AiryAiPrime[z], z] == z AiryAi[z]. Complex arguments evaluate to machine precision (and to arbitrary precision under N[..., n]); AiryAiPrime is Listable.