# recurrence relation with non constant coefficients

I'm trying to solve a second order differential equation and I got a recurrence. Can someone help to solve $$n(n-1+q)a_{n}-a_{n-3}+e\cdot a_{n-2}=0$$ where $q$, $e$, and $a_{0}$ are some real numbers with $a_{1}=0$ and $a_{2}=-e\cdot a_{0}/(2(1+q))$.

-

3
Perhaps you should edit your question so that it looks a little cleaner. Some $a_0$'s just floating in there – Patrick Da Silva Feb 11 '12 at 14:51

1
Recurrences like this don't always have neat solutions. One approach is to calculate the next few terms to see whether there is a pattern. – Gerry Myerson Feb 12 '12 at 0:59
I actually calculate the first six terms, the dependence on n and q clears up but it remains unclear in "e" – mohamed benbitour Feb 12 '12 at 10:13
Maybe if you edit into your question what you have found out about $n$ and $q$, someone will be able to help you with $e$. – Gerry Myerson Feb 13 '12 at 3:55
I'm very hapy becouse I found a solution in "Combinatorics Function technics" hfa1.physics.msstate.edu/064.pdf – mohamed benbitour Feb 15 '12 at 13:49
show 3 more comments
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9398614168167114, "perplexity_flag": "middle"}