relation to Whittaker equation
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11: 28.34 Methods of Computation
§28.34(i) Characteristic Exponents
… ►Solution of the systems of linear algebraic equations (28.4.5)–(28.4.8) and (28.14.4), with the conditions (28.4.9)–(28.4.12) and (28.14.5), by boundary-value methods (§3.6) to determine the Fourier coefficients. Subsequently, the Fourier series can be summed with the aid of Clenshaw’s algorithm (§3.11(ii)). See Meixner and Schäfke (1954, §2.87). This procedure can be combined with §28.34(ii)(d).
12: 13.29 Methods of Computation
13: 20.9 Relations to Other Functions
§20.9 Relations to Other Functions
►§20.9(i) Elliptic Integrals
… ►§20.9(ii) Elliptic Functions and Modular Functions
… ►The relations (20.9.1) and (20.9.2) between and (or ) are solutions of Jacobi’s inversion problem; see Baker (1995) and Whittaker and Watson (1927, pp. 480–485). … ►§20.9(iii) Riemann Zeta Function
…14: 22.16 Related Functions
§22.16 Related Functions
… ►Relation to Elliptic Integrals
… ►Relation to Theta Functions
… ►Relation to the Elliptic Integral
… ►Definition
…15: 28.8 Asymptotic Expansions for Large
16: Errata
This equation was updated to include the definition of Bessel polynomials in terms of Laguerre polynomials and the Whittaker confluent hypergeometric function.
Section: 15.9(v) Complete Elliptic Integrals. Equations: (11.11.9_5), (11.11.13_5), Intermediate equality in (15.4.27) which relates to , (15.4.34), (19.5.4_1), (19.5.4_2) and (19.5.4_3).
The Kronecker delta symbols have been moved furthest to the right, as is common convention for orthogonality relations.
Following a suggestion from James McTavish on 2017-04-06, the recurrence relation was added to Equation (9.7.2).
A number of additions and changes have been made to the metadata to reflect new and changed references as well as to how some equations have been derived.