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1: 28.12 Definitions and Basic Properties

… ►The introduction to the eigenvalues and the functions of general order proceeds as in §§28.2(i), 28.2(ii), and 28.2(iii), except that we now restrict $\widehat{\nu }\ne 0,1$; equivalently $\nu \ne n$. … ►

§28.12(ii) Eigenfunctions ${\mathrm{me}}_{\nu }(z,q)$

… ►For $q=0$, … ► … ►

2: 28.2 Definitions and Basic Properties

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§28.2(vi) Eigenfunctions

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3: 34.11 Higher-Order $3nj$ Symbols

§34.11 Higher-Order $3nj$ Symbols

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4: 10.24 Functions of Imaginary Order

§10.24 Functions of Imaginary Order

… ►and ${\tilde{J}}_{\nu }\left(x\right)$, ${\tilde{Y}}_{\nu }\left(x\right)$ are linearly independent solutions of (10.24.1): … ►In consequence of (10.24.6), when $x$ is large ${\tilde{J}}_{\nu }\left(x\right)$ and ${\tilde{Y}}_{\nu }\left(x\right)$ comprise a numerically satisfactory pair of solutions of (10.24.1); compare §2.7(iv). … … ►

5: 10.45 Functions of Imaginary Order

§10.45 Functions of Imaginary Order

… ►and ${\tilde{I}}_{\nu }\left(x\right)$, ${\tilde{K}}_{\nu }\left(x\right)$ are real and linearly independent solutions of (10.45.1): … ►The corresponding result for ${\tilde{K}}_{\nu }\left(x\right)$ is given by … ► … ►

6: 10.26 Graphics

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§10.26(i) Real Order and Variable

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§10.26(ii) Real Order, Complex Variable

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§10.26(iii) Imaginary Order, Real Variable

… ►

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Figure 10.26.7: ${\tilde{I}}_{1/2}\left(x\right)$, ${\tilde{K}}_{1/2}\left(x\right)$, $0.01\le x\le 3$. Magnify

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Figure 10.26.8: ${\tilde{I}}_1\left(x\right)$, ${\tilde{K}}_1\left(x\right)$, $0.01\le x\le 3$. Magnify

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7: 10.76 Approximations

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Real Variable and Order $:$ Functions

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Real Variable and Order $:$ Zeros

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Real Variable and Order $:$ Integrals

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Complex Variable; Real Order

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Real Variable; Imaginary Order

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8: Bibliography B

… ►

Asymptotic expansions of the modified Bessel function of the third kind of imaginary order. SIAM J. Appl. Math. 15, pp. 1315–1323.

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External Links:

ISSN 0036-1399, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.45.

Encodings:

BibTeX

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Numerical evaluation of the zero-order Hankel transform using Filon quadrature philosophy. Appl. Math. Lett. 9 (5), pp. 21–26.

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External Links:

ISSN 0893-9659, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

… ►

An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy. Comput. Phys. Comm. 21 (3), pp. 297–314.

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External Links:

Document

Referenced by:

§3.10(iii), §33.22(iv).

Encodings:

BibTeX

… ►

Tables of modified Struve functions of orders zero and unity.

ⓘ

Notes:

Part of the Unpublished Mathematical Tables. Reviewed in Math. Comp., v. 18 (1964), no. 86, p. 332.

Referenced by:

3rd item.

Encodings:

BibTeX

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Mathieu functions of general order: Connection formulae, base functions and asymptotic formulae. I–V. Philos. Trans. Roy. Soc. London Ser. A 301, pp. 75–162.

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External Links:

ISSN 0080-4614, FullText, MathReview (J. Meixner), ZentralBlatt

Referenced by:

§28.8(iv).

Encodings:

BibTeX

…

9: 10.77 Software

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§10.77(ii) Bessel Functions–Real Argument and Integer or Half-Integer Order (including Spherical Bessel Functions)

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§10.77(iii) Bessel Functions–Real Order and Argument

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§10.77(vi) Bessel Functions–Imaginary Order and Real Argument

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§10.77(vii) Bessel Functions–Complex Order and Real Argument

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§10.77(viii) Bessel Functions–Complex Order and Argument

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10: 10.3 Graphics

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§10.3(i) Real Order and Variable

… ►

§10.3(ii) Real Order, Complex Variable

… ►

§10.3(iii) Imaginary Order, Real Variable

… ►

►►

Figure 10.3.18: ${\tilde{J}}_1\left(x\right)$, ${\tilde{Y}}_1\left(x\right)$, $0.01\le x\le 10$. Magnify

►

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Figure 10.3.19: ${\tilde{J}}_5\left(x\right)$, ${\tilde{Y}}_5\left(x\right)$, $0.01\le x\le 10$. Magnify