10 Bessel Functions Modified Bessel Functions 10.25 Definitions 10.27 Connection Formulas

§10.26 Graphics

Permalink:: http://dlmf.nist.gov/10.26

§10.26(i) Real Order and Variable
§10.26(ii) Real Order, Complex Variable
§10.26(iii) Imaginary Order, Real Variable

§10.26(i) Real Order and Variable

Notes:: These graphics were produced at NIST.
Keywords:: modified Bessel functions
Permalink:: http://dlmf.nist.gov/10.26.i

Figure 10.26.1: $\mathop{I_{{0}}\/}\nolimits\!\left(x\right)$ , $\mathop{I_{{1}}\/}\nolimits\!\left(x\right)$ , $\mathop{K_{{0}}\/}\nolimits\!\left(x\right)$ , $\mathop{K_{{1}}\/}\nolimits\!\left(x\right)$ , $0\leq x\leq 3$ .

Symbols:: $\mathop{I_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function, $\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function and : real variable
Permalink:: http://dlmf.nist.gov/10.26.F1
Encodings:: pdf, png

Figure 10.26.2: $e^{{-x}}\mathop{I_{{0}}\/}\nolimits\!\left(x\right)$ , $e^{{-x}}\mathop{I_{{1}}\/}\nolimits\!\left(x\right)$ , $e^{{x}}\mathop{K_{{0}}\/}\nolimits\!\left(x\right)$ , $e^{{x}}\mathop{K_{{1}}\/}\nolimits\!\left(x\right)$ , $0\leq x\leq 10$ .

Symbols:: : base of exponential function, $\mathop{I_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function, $\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function and : real variable
Permalink:: http://dlmf.nist.gov/10.26.F2
Encodings:: pdf, png

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Figure 10.26.3: $\mathop{I_{{\nu}}\/}\nolimits\!\left(x\right)$ , $0\leq x\leq 5,0\leq\nu\leq 4$ .

Symbols:: $\mathop{I_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function, : real variable and $\nu$ : complex parameter
Permalink:: http://dlmf.nist.gov/10.26.F3
Encodings:: VRML, X3D, pdf, png

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Figure 10.26.4: $\mathop{K_{{\nu}}\/}\nolimits\!\left(x\right)$ , $0.1\leq x\leq 5,0\leq\nu\leq 4$ .

Symbols:: $\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function, : real variable and $\nu$ : complex parameter
Permalink:: http://dlmf.nist.gov/10.26.F4
Encodings:: VRML, X3D, pdf, png

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Figure 10.26.5: ${\mathop{I_{{\nu}}\/}\nolimits^{{\prime}}}\!\left(x\right)$ , $0\leq x\leq 5,0\leq\nu\leq 4$ .

Symbols:: $\mathop{I_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function, : real variable and $\nu$ : complex parameter
Permalink:: http://dlmf.nist.gov/10.26.F5
Encodings:: VRML, X3D, pdf, png

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Figure 10.26.6: ${\mathop{K_{{\nu}}\/}\nolimits^{{\prime}}}\!\left(x\right)$ , $0.3\leq x\leq 5,0\leq\nu\leq 4$ .

Symbols:: $\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Bessel function, : real variable and $\nu$ : complex parameter
Permalink:: http://dlmf.nist.gov/10.26.F6
Encodings:: VRML, X3D, pdf, png

§10.26(ii) Real Order, Complex Variable

Permalink:: http://dlmf.nist.gov/10.26.ii

Apply (10.27.6) and (10.27.8) to §10.3(ii).

§10.26(iii) Imaginary Order, Real Variable

Notes:: These graphs were produced at NIST.
Referenced by:: §10.45
Permalink:: http://dlmf.nist.gov/10.26.iii

For the notation, see §10.45.

Figure 10.26.7: $\mathop{\widetilde{I}_{{1/2}}\/}\nolimits\!\left(x\right),\mathop{\widetilde{K% }_{{1/2}}\/}\nolimits\!\left(x\right),0.01\leq x\leq 3$ .

Symbols:: $\mathop{\widetilde{I}_{{\nu}}\/}\nolimits\!\left(x\right)$ : modified Bessel function of imaginary order, $\mathop{\widetilde{K}_{{\nu}}\/}\nolimits\!\left(x\right)$ : modified Bessel function of imaginary order and : real variable
Keywords:: modified Bessel functions
Permalink:: http://dlmf.nist.gov/10.26.F7
Encodings:: pdf, png

Figure 10.26.8: $\mathop{\widetilde{I}_{{1}}\/}\nolimits\!\left(x\right),\mathop{\widetilde{K}_% {{1}}\/}\nolimits\!\left(x\right),0.01\leq x\leq 3$ .

Symbols:: $\mathop{\widetilde{I}_{{\nu}}\/}\nolimits\!\left(x\right)$ : modified Bessel function of imaginary order, $\mathop{\widetilde{K}_{{\nu}}\/}\nolimits\!\left(x\right)$ : modified Bessel function of imaginary order and : real variable
Keywords:: modified Bessel functions
Permalink:: http://dlmf.nist.gov/10.26.F8
Encodings:: pdf, png

Figure 10.26.9: $\mathop{\widetilde{I}_{{5}}\/}\nolimits\!\left(x\right),\mathop{\widetilde{K}_% {{5}}\/}\nolimits\!\left(x\right),0.01\leq x\leq 3$ .