modified Bessel equation
(0.008 seconds)
11—20 of 66 matching pages
11: 10.1 Special Notation
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►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
12: 10.38 Derivatives with Respect to Order
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10.38.1
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13: 10.44 Sums
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§10.44(i) Multiplication Theorem
… ►§10.44(ii) Addition Theorems
… ►Graf’s and Gegenbauer’s Addition Theorems
… ►§10.44(iii) Neumann-Type Expansions
… ►§10.44(iv) Compendia
…14: 10.47 Definitions and Basic Properties
15: 10.40 Asymptotic Expansions for Large Argument
§10.40 Asymptotic Expansions for Large Argument
►§10.40(i) Hankel’s Expansions
… ►Products
… ► … ►§10.40(iv) Exponentially-Improved Expansions
…16: 18.34 Bessel Polynomials
§18.34 Bessel Polynomials
… ►where is a modified spherical Bessel function (10.49.9), and … … ►§18.34(ii) Orthogonality
… ►§18.34(iii) Other Properties
…17: Errata
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Equation (18.12.2)
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Equation (18.34.2)
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Equations (10.15.1), (10.38.1)
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18.12.2
This equation was updated to include on the left-hand side, its definition in terms of a product of two functions.
18.34.2
This equation was updated to include definitions in terms of the modified spherical Bessel function of the second kind.
These equations have been generalized to include the additional cases of , , respectively.
18: 10.27 Connection Formulas
§10.27 Connection Formulas
►Other solutions of (10.25.1) are and . ►
10.27.1
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10.27.3
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►Many properties of modified Bessel functions follow immediately from those of ordinary Bessel functions by application of (10.27.6)–(10.27.8).
19: 10.35 Generating Function and Associated Series
§10.35 Generating Function and Associated Series
… ►Jacobi–Anger expansions: for , … ►
10.35.4
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