case λ=0
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11—20 of 128 matching pages
11: 20.11 Generalizations and Analogs
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►In the case
identities for theta functions become identities in the complex variable , with , that involve rational functions, power series, and continued fractions; see Adiga et al. (1985), McKean and Moll (1999, pp. 156–158), and Andrews et al. (1988, §10.7).
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12: 28.35 Tables
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Blanch and Clemm (1965) includes values of , for , ; , . Also , for , ; , . In all cases . Precision is generally 7D. Approximate formulas and graphs are also included.
13: 10.67 Asymptotic Expansions for Large Argument
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§10.67(ii) Cross-Products and Sums of Squares in the Case
…14: 28.4 Fourier Series
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§28.4(iv) Case
…15: 30.2 Differential Equations
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►This equation has regular singularities at with exponents and an irregular singularity of rank 1 at (if ).
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►With Equation (30.2.1) changes to
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§30.2(iii) Special Cases
►If , Equation (30.2.1) is the associated Legendre differential equation; see (14.2.2). …If , Equation (30.2.4) is satisfied by spherical Bessel functions; see (10.47.1).16: 32.8 Rational Solutions
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►In the general case assume , so that as in §32.2(ii) we may set and .
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►In the general case assume , so that as in §32.2(ii) we may set .
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►For the case
see Airault (1979) and Lukaševič (1968).
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17: 18.14 Inequalities
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18.14.3_5
, .
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18.14.8
, .
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►The case
of (18.14.26) is the Askey–Gasper inequality (18.38.3).
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18: 19.26 Addition Theorems
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§19.26(ii) Case
…19: 19.17 Graphics
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►The cases
or correspond to the complete integrals.
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