The Journal of the Indian Mathematical Society

V. L. Mutatker ¹

Affiliations
1 Allahabad, IN

Abstract

In Art. 1 of the present paper the summation formula is found, in Art. 2, some expansions in terms of the parabolic cylinder functions are obtained, and in Art. 3 certain integrals involving D_n (z) are evaluated.

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V. L. Mutatker ¹

Affiliations
1 Allahabad University, IN

Abstract

In the present paper, I seek to express ξ(s)II_p/k (1-¹ /_p^s,) , (where  p\k means that p runs through all the prime divisors of k), in the form of definite integrals and contour integrals of the Hankel type.

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V. L. Mutatker ¹

Affiliations
1 Allahabad, IN

Abstract

In Art. 1 of the present paper certain indefinite integrals involving D_n(z) are evaluated, in Art. 2 the expansion of the product D_g(z) D_m(z) D_n(z) is obtained in series of the functions D_n(z), in Art, 3 the integral ∫D₀(z) D_p(z) D_m(z) D_n(z) dz is evaluated and in Art, 4 an Addition theorem is found.

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