confluent hypergeometric functions
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1: 35.6 Confluent Hypergeometric Functions of Matrix Argument
§35.6 Confluent Hypergeometric Functions of Matrix Argument
►§35.6(i) Definitions
… ►Laguerre Form
… ►§35.6(ii) Properties
… ►§35.6(iv) Asymptotic Approximations
…2: 6.11 Relations to Other Functions
3: 13.28 Physical Applications
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§13.28(i) Exact Solutions of the Wave Equation
… ►For potentials in quantum mechanics that are solvable in terms of confluent hypergeometric functions see Negro et al. (2000). … ►§13.28(iii) Other Applications
…4: 13.27 Mathematical Applications
§13.27 Mathematical Applications
►Confluent hypergeometric functions are connected with representations of the group of third-order triangular matrices. … …5: 12.20 Approximations
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►Luke (1969b, pp. 25 and 35) gives Chebyshev-series expansions for the confluent hypergeometric functions
and (§13.2(i)) whose regions of validity include intervals with endpoints and , respectively.
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6: 8.5 Confluent Hypergeometric Representations
§8.5 Confluent Hypergeometric Representations
►For the confluent hypergeometric functions , , , and the Whittaker functions and , see §§13.2(i) and 13.14(i). … ►
8.5.2
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8.5.3
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8.5.5
7: 13.6 Relations to Other Functions
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§13.6(ii) Incomplete Gamma Functions
… ►§13.6(iii) Modified Bessel Functions
… ►§13.6(iv) Parabolic Cylinder Functions
… ►Hermite Polynomials
… ►Laguerre Polynomials
…8: 13.18 Relations to Other Functions
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