large degree
(0.001 seconds)
21—29 of 29 matching pages
21: 8.27 Approximations
DiDonato (1978) gives a simple approximation for the function (which is related to the incomplete gamma function by a change of variables) for real and large positive . This takes the form , approximately, where and is shown to produce an absolute error as .
Verbeeck (1970) gives polynomial and rational approximations for , approximately, where denotes a quotient of polynomials of equal degree in .
22: 12.10 Uniform Asymptotic Expansions for Large Parameter
§12.10 Uniform Asymptotic Expansions for Large Parameter
… ►§12.10(vi) Modifications of Expansions in Elementary Functions
… ► … ►Modified Expansions
… ►23: 10.41 Asymptotic Expansions for Large Order
§10.41 Asymptotic Expansions for Large Order
►§10.41(i) Asymptotic Forms
… ►§10.41(ii) Uniform Expansions for Real Variable
… ► … ►24: 24.16 Generalizations
25: DLMF Project News
error generating summary26: 28.35 Tables
National Bureau of Standards (1967) includes the eigenvalues , for with , and with ; Fourier coefficients for and for , , respectively, and various values of in the interval ; joining factors , for with (but in a different notation). Also, eigenvalues for large values of . Precision is generally 8D.
Zhang and Jin (1996, pp. 533–535) includes the zeros (in degrees) of , for , and the first 5 zeros of , for or , . Precision is mostly 9S.