Whittaker equation
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11—20 of 60 matching pages
11: 22.13 Derivatives and Differential Equations
§22.13 Derivatives and Differential Equations
… ►§22.13(ii) First-Order Differential Equations
… ►§22.13(iii) Second-Order Differential Equations
…12: 13.18 Relations to Other Functions
13: 31.8 Solutions via Quadratures
14: 13.29 Methods of Computation
§13.29(ii) Differential Equations
… ►For and this means that in the sector we may integrate along outward rays from the origin with initial values obtained from (13.2.2) and (13.14.2). ►For and we may integrate along outward rays from the origin in the sectors , with initial values obtained from connection formulas in §13.2(vii), §13.14(vii). … ►The integral representations (13.4.1) and (13.4.4) can be used to compute the Kummer functions, and (13.16.1) and (13.16.5) for the Whittaker functions. …15: 18.39 Applications in the Physical Sciences
Other Analytically Solved Schrödinger Equations
…16: 5.9 Integral Representations
17: Errata
This equation was updated to include the definition of Bessel polynomials in terms of Laguerre polynomials and the Whittaker confluent hypergeometric function.
Originally the in front of the was given incorrectly as .
Reported 2017-02-02 by Daniel Karlsson.
A sentence was added in §8.18(ii) to refer to Nemes and Olde Daalhuis (2016). Originally §8.11(iii) was applicable for real variables and . It has been extended to allow for complex variables and (and we have replaced with in the subsection heading and in Equations (8.11.6) and (8.11.7)). Also, we have added two paragraphs after (8.11.9) to replace the original paragraph that appeared there. Furthermore, the interval of validity of (8.11.6) was increased from to the sector , and the interval of validity of (8.11.7) was increased from to the sector , . A paragraph with reference to Nemes (2016) has been added in §8.11(v), and the sector of validity for (8.11.12) was increased from to . Two new Subsections 13.6(vii), 13.18(vi), both entitled Coulomb Functions, were added to note the relationship of the Kummer and Whittaker functions to various forms of the Coulomb functions. A sentence was added in both §13.10(vi) and §13.23(v) noting that certain generalized orthogonality can be expressed in terms of Kummer functions.
Originally the left-hand side was given correctly as ; the equation is true also for .