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Varma, R. S.
- On a Certain Polynomial Analogous to Lommel's Polynomial
Authors
1 Christ Church College, Cawnpore, IN
Source
The Journal of the Indian Mathematical Society, Vol 19 (1932), Pagination: 274-278Abstract
In a recent paper*, Dr. S. C. Mitra has shown that the Parabolic cylinder function, Dn (z), satisfies the relation
Dm+n (x) + ( - 1)n (n + 1) Rn, m-2, (x) Dn (x)
+ ( - l )m = Rn-1,m-1 (x) Dn +1 (x) = 0, … (1)
where Rn,m (x) is a polynomial analogous to that of Lommelt in the theory of Bessel Functions.
- Some Infinite Integrals Involving Weber's Parabolic Cylinder Functions
Authors
1 Christ Church College, Cawnpore, IN
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 25-33Abstract
The object of this paper is to evaluate some infinite integrals involving Weber's parabolic cylinder functions. Thus in 2, an integral involving a Whittaker function Wk,m(x) and a Kummer function 1F1 is investigated.- On Laguerre's Polynomials which are Self-Reciprocal in the Hankel Transform
Authors
1 Cawnpore, IN
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 54-55Abstract
On Laguerre's Polynomials which are Self-Reciprocal in the Hankel Transform.- Some Infinite Series Involving Sonine's Polynomial
Authors
1 Lucknow University, IN
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 330-333Abstract
In general we can have two types of infinite series involving the polynomial:
Σ arTrm(x) (A)
and
Σ brTrn(x) (B).
Series of the type (A) have been discussed extensively from time to time by various authors, but very little is known about series of the type (B).
- Extensions of Some Self-Reciprocal Functions
Authors
Source
The Journal of the Indian Mathematical Society, Vol 2 (1937), Pagination: 269-275Abstract
In a recent paper I have shown that the functions
xv+1/2e1/4x2D-2r-3(x) R(v)>-1
and
xv-1/2e1/4x2D-2r(x) R(v)>-1/2
are self-reciprocal in the Hankel-transform of order v.
- "On a Certain Polynomial Analogous to Lommel's Polynomial"
Authors
1 Christ Church College, Cawnpore, IN