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1: 16.7 Relations to Other Functions

§16.7 Relations to Other Functions

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2: 6.11 Relations to Other Functions

§6.11 Relations to Other Functions

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Incomplete Gamma Function

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Confluent Hypergeometric Function

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6.11.2 $$E_1\left(z\right)={\mathrm{e}}^{-z}U(1,1,z),$$

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Symbols:

$U(a,b,z)$: Kummer confluent hypergeometric function, $\mathrm{e}$: base of natural logarithm, $E_1\left(z\right)$: exponential integral and $z$: complex variable

Referenced by:

§6.11, 5th item, §6.6

Permalink:

http://dlmf.nist.gov/6.11.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §6.11, §6.11 and Ch.6

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3: 8.16 Generalizations

… ►Other generalizations are considered in Guthmann (1991) and Paris (2003).

4: 26.20 Physical Applications

… ►Other articles on this subject are de Bruijn (1981) and Rouvray (1995). The latter reference also describes chemical applications of other combinatorial techniques. ►Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). … ►Other applications to problems in engineering, crystallography, biology, and computer science can be found in Beckenbach (1981) and Graham et al. (1995).

5: 18.40 Methods of Computation

… ►Usually, however, other methods are more efficient, especially the numerical solution of difference equations (§3.6) and the application of uniform asymptotic expansions (when available) for OP’s of large degree. ►However, for applications in which the OP’s appear only as terms in series expansions (compare §18.18(i)) the need to compute them can be avoided altogether by use instead of Clenshaw’s algorithm (§3.11(ii)) and its straightforward generalization to OP’s other than Chebyshev. …

6: 32.1 Special Notation

… ►(For other notation see Notation for the Special Functions.) …

7: 4.44 Other Applications

§4.44 Other Applications

… ►For other applications of the Lambert $W$-function see Corless et al. (1996).

8: 11.16 Software

… ►References to research software that is available in other ways is listed separately. … ►For other software see the Software Index. … ►For other software see the Software Index. … ►For other software see the Software Index. … ►For other software see the Software Index.

9: 1.1 Special Notation

… ►(For other notation see Notation for the Special Functions.) …

10: 17.16 Mathematical Applications

… ►These and other applications are described in the surveys Andrews (1974, 1986). …