A new Ramanujan-type identity for $$L(2k+1, \chi _1)$$

One of the celebrated formulas Ramanujan is about odd zeta values, which has been studied by many mathematicians over years. A notable extension was given Grosswald in 1972. Following Ramanujan’s idea, we rediscovered a Ramanujan-type identity for $$\zeta (2k+1)$$ that first established Malurkar and later Berndt using different techniques. In current paper, extend aforementioned to derive new $$L(2k+1, \chi _1)$$ , where $$\chi _1$$ principal character modulo prime p. process, encounter family polynomials. Furthermore, establish analogue Grosswald’s identity.