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A CONTINUED FRACTION FROM UNORGANIZED PORTIONS OF RAMANUJAN’S NOTEBOOKS AND PARTITIONS
Bhaskar Srivastava 충청수학회 2005 충청수학회지 Vol.18 No.1
In this paper, we consider the finite form of the continued fraction found in the unorganized material, Entry 9 [2], and give the sum of n terms. We give the n th convergent series in two ways-one by simple expansion and the other by using partition theory.
A STUDY OF THE BILATERAL FORM OF THE MOCK THETA FUNCTIONS OF ORDER EIGHT
Bhaskar Srivastava 충청수학회 2005 충청수학회지 Vol.18 No.2
We give a generalization of bilateral mock theta functions of order eight and show that they are F q -functions. We also give an integral representation for these functions. We give a relation between mock theta functions of the first set and bilateral mock theta functions of the second set.
REDUCIBILITY, MULTIBASIC EXPANSION AND INTEGRAL REPRESENTATION FOR BASIC APPELL FUNCTIONS
Bhaskar Srivastava 충청수학회 2005 충청수학회지 Vol.18 No.2
We give bibasic expansion for basic Appell functions Φ (1) and Φ (2) , and their integral representations. We also give a continued fraction representation for Φ (2) .
Ramanujan's Continued Fraction, a Generalization and Partitions
Srivastava, Bhaskar Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.2
We generalize a continued fraction of Ramanujan by introducing a free parameter. We give the closed form for the continued fraction. We also consider the finite form giving $n^{th}$ convergent using partition theory.
The Fourth and Eighth Order Mock Theta Functions
Srivastava, Bhaskar Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.1
In the paper we consider deemed three mock theta functions introduced by Hikami. We have given their alternative expressions in double summation analogous to Hecke type expansion. In proving we also give a new Bailey pair relative to $a^2$. I presume they will be helpful in getting fundamental transformations.
A Note on an Analogous Continued Fraction of Ramanujan
Srivastava, Bhaskar Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.4
We give an integral representation for an analogous continued fraction of Ramanujan, for this we first prove an interesting identity.
REDUCIBILITY, MULTIBASIC EXPANSION AND INTEGRAL REPRESENTATION FOR BASIC APPELL FUNCTIONS
Srivastava, Bhaskar 충청수학회 2005 충청수학회지 Vol.18 No.2
We give bibasic expansion for basic Appell functions ${\Phi}^{(1)}$ and ${\Phi}^{(2)}$, and their integral representations. We also give a continued fraction representation for ${\Phi}^{(2)}$.
A STUDY OF THE BILATERAL FORM OF THE MOCK THETA FUNCTIONS OF ORDER EIGHT
Srivastava, Bhaskar 충청수학회 2005 충청수학회지 Vol.18 No.2
We give a generalization of bilateral mock theta functions of order eight and show that they are $F_q$-functions. We also give an integral representation for these functions. We give a relation between mock theta functions of the first set and bilateral mock theta functions of the second set.
PARTIAL SECOND ORDER MOCK THETA FUNCTIONS, THEIR EXPANSIONS AND PADE APPROXIMANTS
Srivastava, Bhaskar Korean Mathematical Society 2007 대한수학회지 Vol.44 No.4
By proving a summation formula, we enumerate the expansions for the mock theta functions of order 2 in terms of partial mock theta functions of order 2, 3 and 6. We show a relation between Ramanujan's ${\mu}(q)$-function and his sixth order mock theta functions. In addition, we also give the continued fraction representation for ${\mu}(q)$ and 2nd order mock theta functions and $Pad\acute{e}$ approximants.
SOME EISENSTEIN SERIES IDENTITIES RELATED TO MODULAR EQUATION OF THE FOURTH ORDER
Srivastava, Bhaskar Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.1
We find some Eisenstein series related to modulus 4 using a theta function identity of McCullough and Shen and residue theorem for elliptic functions.