Generalized elliptic integrals and modular equations
نویسندگان
چکیده
منابع مشابه
Generalized Elliptic Integrals and Modular Equations
In geometric function theory, generalized elliptic integrals and functions arise from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to Gaussian hypergeometric functions. Certain combinations of these integrals also occur in analytic number theory in the study of Ramanujan’s modular equations and approximations to π. The authors stu...
متن کاملGeneralized Integrals and Differential Equations.
in which a and b are continuously differentiate functions of two variables, fix) a continuously difierentiable function. The routine estimate of fadb gives bounds depending either on /| d/(x) | or on the maximum of | df/dx\ in the interval of integration. It is, however, possible, as shown in Theorem 1, to give a bound that is entirely independent'of the derivative of fix), and, consequently, t...
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A number of families of elliptic-type integrals have been studied recently due to their importance and potential for applications in some problems of radiation physics. The object of this work is to present a unified and generalized form of such elliptic-type integrals and to study its properties, including recurrence formulas and asymptotic expansion.
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Let p ≥ 5 be a prime. We show that the space of weight one Eisenstein series defines an embedding into P(p−3)/2 of the modular curve X1(p) for the congruence group Γ1(p) that is scheme-theoretically cut out by explicit quadratic equations.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2000
ISSN: 0030-8730
DOI: 10.2140/pjm.2000.192.1