as x→±1
(0.040 seconds)
11—20 of 626 matching pages
11: 30.7 Graphics
12: 12.19 Tables
Abramowitz and Stegun (1964, Chapter 19) includes and for , , 5S; for , , 4-5D or 4-5S.
Miller (1955) includes , , and reduced derivatives for , , 8D or 8S. Modulus and phase functions, and also other auxiliary functions are tabulated.
Fox (1960) includes modulus and phase functions for and , and several auxiliary functions for , , 8S.
Kireyeva and Karpov (1961) includes for , , and , , 7D.
Murzewski and Sowa (1972) includes for , , 7S.
13: 6.19 Tables
Abramowitz and Stegun (1964, Chapter 5) includes , , , , ; , , , , ; , , , , ; , , , , ; , , . Accuracy varies but is within the range 8S–11S.
Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of , , , 6D; , , , 6D; , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.
14: 14.33 Tables
Abramowitz and Stegun (1964, Chapter 8) tabulates for , , 5–8D; for , , 5–7D; and for , , 6–8D; and for , , 6S; and for , , 6S. (Here primes denote derivatives with respect to .)
Zhang and Jin (1996, Chapter 4) tabulates for , , 7D; for , , 8D; for , , 8S; for , , 8D; for , , , , 8S; for , , 8S; for , , , 5D; for , , 7S; for , , 8S. Corresponding values of the derivative of each function are also included, as are 6D values of the first 5 -zeros of and of its derivative for , .
Žurina and Karmazina (1963) tabulates the conical functions for , , 7S; for , , 7S. Auxiliary tables are included to assist computation for larger values of when .
15: 18.6 Symmetry, Special Values, and Limits to Monomials
16: 18.5 Explicit Representations
17: 14.3 Definitions and Hypergeometric Representations
§14.3(i) Interval
►The following are real-valued solutions of (14.2.2) when , and . … ►§14.3(ii) Interval
►The following are solutions of (14.2.2) when , and . … ►Like , but unlike , is real-valued when , and , and is defined for all values of and . …18: 5.23 Approximations
19: 16.14 Partial Differential Equations
20: 10.75 Tables
The main tables in Abramowitz and Stegun (1964, Chapter 9) give to 15D, , , , to 10D, to 8D, ; , , , 8D; , , , , 5D or 5S; , , , , 10S; modulus and phase functions , , , , 8D.
Achenbach (1986) tabulates , , , , , 20D or 18–20S.
Achenbach (1986) tabulates , , , , , 19D or 19–21S.
Bickley and Nayler (1935) tabulates (§10.43(iii)) for , 2, 3, 9D.